Intellect_city - World Cycle - Ath - Timeframe 1D and 1WIndicator Overview
The Pi Cycle Top Indicator has historically been effective in picking out the timing of market cycle highs within 3 days.
It uses the 111 day moving average (111DMA) and a newly created multiple of the 350 day moving average, the 350DMA x 2.
Note: The multiple is of the price values of the 350DMA, not the number of days.
For the past three market cycles, when the 111DMA moves up and crosses the 350DMA x 2 we see that it coincides with the price of Bitcoin peaking.
It is also interesting to note that 350 / 111 is 3.153, which is very close to Pi = 3.142. In fact, it is the closest we can get to Pi when dividing 350 by another whole number.
It once again demonstrates the cyclical nature of Bitcoin price action over long time frames. However, in this instance, it does so with a high degree of accuracy over Bitcoin's adoption phase of growth.
Bitcoin Price Prediction Using This Tool
The Pi Cycle Top Indicator forecasts the cycle top of Bitcoin’s market cycles. It attempts to predict the point where Bitcoin price will peak before pulling back. It does this on major high time frames and has picked the absolute tops of Bitcoin’s major price moves throughout most of its history.
How It Can Be Used
Pi Cycle Top is useful to indicate when the market is very overheated. So overheated that the shorter-term moving average, which is the 111-day moving average, has reached an x2 multiple of the 350-day moving average. Historically, it has proved advantageous to sell Bitcoin around this time in Bitcoin's price cycles.
It is also worth noting that this indicator has worked during Bitcoin's adoption growth phase, the first 15 years or so of Bitcoin's life. With the launch of Bitcoin ETF's and Bitcoin's increased integration into the global financial system, this indicator may cease to be relevant at some point in this new market structure.
Cerca negli script per "Cycle"
Financial Astrology Saturn LongitudeSaturn energy strengthen the temperance, rectitude, constancy, greed, pessimism and precautionary. Under this influence the crowd will move with caution, slow and with strong and rigorous sense, analysing the environment in detail and deducting all the possible action outcomes based on the past experiences and utilising all the accesible wisdom. This cycle rules the land and real state, the state and institutions, officials, and regulations.
Due to the essential nature of this energy is expected that traders take more caution and reflexion in their investment decisions where Saturn transits through earth element (Taurus, Virgo, Capricorn) because the persons become more prudent and rigid. In water elements (Cancer, Scorpio and Pisces) traders will be reducing exposure to risky assets because the emotions are more unstable and the fear to loss results in risk aversion.
This cycle takes 29 years to complete so we don't have enough observations in the crypto-currencies sector to evaluate the potential effect of Saturn through all the zodiac signs but with the historical data available, there are some interesting patterns: the most bearish zodiac signs was Scorpio (water) and Capricorn (earth) and the most bullish was Sagittarius and Aquarius. This correlates well with other planet cycles where we have observed that air zodiac signs are usually bullish.
This indicator provides longitude since 2010 so will be limited in the zodiac signs that is possible to be analysed, however the periods of retrogradation and stationary speed phases could give interesting trading signals. We encourage you to analyse this cycles in different markets and share with us your observations, leave us a comment with your research outcomes. Happy research!
Note: The Saturn tropical longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the longitude is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart reference timezone.
Ehlers Adaptive Center Of Gravity [CC]The Adaptive Center Of Gravity was created by John Ehlers and this is a regular center of gravity indicator combined to be use with the current cycle period. If you are not familiar with stock cycles then I would highly recommend his book on the subject: Cycle Analytics. Buy when the indicator turns green and sell when it turns red.
Let me know if there are any other indicators you want me to publish!
Bitcoin Logarithmic Growth Curve 2024The Bitcoin logarithmic growth curve is a concept used to analyze Bitcoin's price movements over time. The idea is based on the observation that Bitcoin's price tends to grow exponentially, particularly during bull markets. It attempts to give a long-term perspective on the Bitcoin price movements.
The curve includes an upper and lower band. These bands often represent zones where Bitcoin's price is overextended (upper band) or undervalued (lower band) relative to its historical growth trajectory. When the price touches or exceeds the upper band, it may indicate a speculative bubble, while prices near the lower band may suggest a buying opportunity.
Unlike most Bitcoin growth curve indicators, this one includes a logarithmic growth curve optimized using the latest 2024 price data, making it, in our view, superior to previous models. Additionally, it features statistical confidence intervals derived from linear regression, compatible across all timeframes, and extrapolates the data far into the future. Finally, this model allows users the flexibility to manually adjust the function parameters to suit their preferences.
The Bitcoin logarithmic growth curve has the following function:
y = 10^(a * log10(x) - b)
In the context of this formula, the y value represents the Bitcoin price, while the x value corresponds to the time, specifically indicated by the weekly bar number on the chart.
How is it made (You can skip this section if you’re not a fan of math):
To optimize the fit of this function and determine the optimal values of a and b, the previous weekly cycle peak values were analyzed. The corresponding x and y values were recorded as follows:
113, 18.55
240, 1004.42
451, 19128.27
655, 65502.47
The same process was applied to the bear market low values:
103, 2.48
267, 211.03
471, 3192.87
676, 16255.15
Next, these values were converted to their linear form by applying the base-10 logarithm. This transformation allows the function to be expressed in a linear state: y = a * x − b. This step is essential for enabling linear regression on these values.
For the cycle peak (x,y) values:
2.053, 1.268
2.380, 3.002
2.654, 4.282
2.816, 4.816
And for the bear market low (x,y) values:
2.013, 0.394
2.427, 2.324
2.673, 3.504
2.830, 4.211
Next, linear regression was performed on both these datasets. (Numerous tools are available online for linear regression calculations, making manual computations unnecessary).
Linear regression is a method used to find a straight line that best represents the relationship between two variables. It looks at how changes in one variable affect another and tries to predict values based on that relationship.
The goal is to minimize the differences between the actual data points and the points predicted by the line. Essentially, it aims to optimize for the highest R-Square value.
Below are the results:
It is important to note that both the slope (a-value) and the y-intercept (b-value) have associated standard errors. These standard errors can be used to calculate confidence intervals by multiplying them by the t-values (two degrees of freedom) from the linear regression.
These t-values can be found in a t-distribution table. For the top cycle confidence intervals, we used t10% (0.133), t25% (0.323), and t33% (0.414). For the bottom cycle confidence intervals, the t-values used were t10% (0.133), t25% (0.323), t33% (0.414), t50% (0.765), and t67% (1.063).
The final bull cycle function is:
y = 10^(4.058 ± 0.133 * log10(x) – 6.44 ± 0.324)
The final bear cycle function is:
y = 10^(4.684 ± 0.025 * log10(x) – -9.034 ± 0.063)
The main Criticisms of growth curve models:
The Bitcoin logarithmic growth curve model faces several general criticisms that we’d like to highlight briefly. The most significant, in our view, is its heavy reliance on past price data, which may not accurately forecast future trends. For instance, previous growth curve models from 2020 on TradingView were overly optimistic in predicting the last cycle’s peak.
This is why we aimed to present our process for deriving the final functions in a transparent, step-by-step scientific manner, including statistical confidence intervals. It's important to note that the bull cycle function is less reliable than the bear cycle function, as the top band is significantly wider than the bottom band.
Even so, we still believe that the Bitcoin logarithmic growth curve presented in this script is overly optimistic since it goes parly against the concept of diminishing returns which we discussed in this post:
This is why we also propose alternative parameter settings that align more closely with the theory of diminishing returns.
Our recommendations:
Drawing on the concept of diminishing returns, we propose alternative settings for this model that we believe provide a more realistic forecast aligned with this theory. The adjusted parameters apply only to the top band: a-value: 3.637 ± 0.2343 and b-parameter: -5.369 ± 0.6264. However, please note that these values are highly subjective, and you should be aware of the model's limitations.
Conservative bull cycle model:
y = 10^(3.637 ± 0.2343 * log10(x) - 5.369 ± 0.6264)
[blackcat] L2 Ehlers Dominant Cycle Tuned Bandpass FilterLevel: 2
Background
John F. Ehlers introuced his Dominant Cycle Tuned Bandpass Filter Strategy in Mar, 2008.
Function
In "Measuring Cycle Periods", author John Ehlers presents a very interesting technique of measuring dominant market cycle periods by means of multiple bandpass filtering. By utilizing an approach similar to audio equalizers, the signal (here, the price series) is fed into a set of simple second-order infinite impulse response bandpass filters. Filters are tuned to 8,9,10,...,50 periods. The filter with the highest output represents the dominant cycle. A full-featured formula that implements a high-pass filter and a six-tap low-pass Fir filter on input, then 42 parallel Iir band-pass filters.
I've coded John Ehlers' filter bank to measure the dominant cycle (DC) and the sine and cosine filter components in pine v4 for TradingView, based on John Ehlers' article in this issue, "Measuring Cycle Periods." The CycleFilterDC function plots and returns the DC series and its components, so it's a trivial matter to make use of them in a trading strategy.
Based on John Ehlers' article, "Measuring Cycle Periods," he chose to implement the dominant cycle-tuned bandpass filter response to test Ehlers' suggestion to use the sine and cosine crossovers as buy and sell signals. If the sine closely follows the price pattern as suggested, and the cosine is an effective leading function of the sine, then it seems to make sense that a crossover implementation would work well (Personally, what I observed this is not so accurated as his claims).
What he discovered in his tests was that crossovers happened at frequent intervals, even when price has not moved significantly. This leads to a higher percentage of losing trades, particularly when spread, slippage, and commissions are accounted for. Nevertheless, the cosine crossover was quite effective at identifying reversals very early in many cases, so this indicator could prove quite effective when used alongside other indicators. In particular, the use of an indicator to confirm a certain level of recent volatility, as well as an indicator to confirm significant rate of change, could prove quite helpful.
Key Signal
CosineLine--> Ehlers Dominant Cycle Tuned Bandpass Filter Strategy fast line
SineLine--> Ehlers Dominant Cycle Tuned Bandpass Filter Strategy slow line
Pros and Cons
100% John F. Ehlers definition translation, even variable names are the same. This help readers who would like to use pine to read his book.
Remarks
The 72th script for Blackcat1402 John F. Ehlers Week publication.
NOTE: Although Dr. Ehlers think high of Cosine and Sine wave indicator and trading strategy, my study and trading experience indicated it did not work that well as many other oscillator indicators. However, I would like to keep the original code of Dr. Ehlers for anyone who want to make a deep dive into this kind of indicator or strategy with Cosine and Sine wave.
Readme
In real life, I am a prolific inventor. I have successfully applied for more than 60 international and regional patents in the past 12 years. But in the past two years or so, I have tried to transfer my creativity to the development of trading strategies. Tradingview is the ideal platform for me. I am selecting and contributing some of the hundreds of scripts to publish in Tradingview community. Welcome everyone to interact with me to discuss these interesting pine scripts.
The scripts posted are categorized into 5 levels according to my efforts or manhours put into these works.
Level 1 : interesting script snippets or distinctive improvement from classic indicators or strategy. Level 1 scripts can usually appear in more complex indicators as a function module or element.
Level 2 : composite indicator/strategy. By selecting or combining several independent or dependent functions or sub indicators in proper way, the composite script exhibits a resonance phenomenon which can filter out noise or fake trading signal to enhance trading confidence level.
Level 3 : comprehensive indicator/strategy. They are simple trading systems based on my strategies. They are commonly containing several or all of entry signal, close signal, stop loss, take profit, re-entry, risk management, and position sizing techniques. Even some interesting fundamental and mass psychological aspects are incorporated.
Level 4 : script snippets or functions that do not disclose source code. Interesting element that can reveal market laws and work as raw material for indicators and strategies. If you find Level 1~2 scripts are helpful, Level 4 is a private version that took me far more efforts to develop.
Level 5 : indicator/strategy that do not disclose source code. private version of Level 3 script with my accumulated script processing skills or a large number of custom functions. I had a private function library built in past two years. Level 5 scripts use many of them to achieve private trading strategy.
Strength Analyzer [DW]This is an experimental hybrid between relative strength and spectrum analysis methods aimed to deliver useful insights about cyclical dominance and momentum.
This study utilizes a modified RSI formula and a modified Goertzel algorithm to determine relative strength and spectral dominance for periods 8 through 50.
These periods are theorized by many analysts to be the main cyclical components of market movement.
In this study, you are given the option to apply equalization (EQ) to the dataset before estimating strength.
This enables you to transform your data and observe how strength estimates changes as well.
Whether you want to give emphasis to some frequencies, isolate specific bands, or completely alter the shape of your waveform, EQ filtration makes for an interesting experience.
The default EQ preset in this script cuts low end presence, dampens high frequency oscillations, and cleanly passes main cyclic components.
There are many ways to use EQ to transform your dataset, so play around with the settings and find the presets that work best for your analysis setup.
After EQ processing, the data is then passed through the modified RSI algorithm to generate momentum information
The modified RSI in this script is rescaled to oscillate between -1 and 1, and has the option to pass through a 2 pole Butterworth low pass filter before and after processing for a smoother output.
The strength thresholds are determined by the threshold value, which quantifies distance above and below 0.
The threshold value can also be thought of as conventional RSI distance from 50 rescaled so that an increment of 0.1 is equivalent to an increment of 5 on a conventional RSI.
A threshold value of 0.4 is equivalent to thresholds of 70 and 30 on a conventional RSI, so this is the default. The maximum threshold value is 1, which is equivalent to thresholds of 100 and 0.
This script plots colored sections for each period value using a gradient color scheme based on their respective strength estimates.
The color scheme in this script is a multicolored gradient that shows green scaled colors for bullish strength and red scaled colors for bearish strength.
Darker, less vibrant colors indicate lower strength. Brighter, more vibrant colors indicate higher strength.
Strength values near 0 will show the darkest colors, and values near the positive or negative threshold value will show the brightest.
The data is fed parallel through the modified Goertzel algorithm to obtain cyclic power information and to estimate the dominant cycle.
Gerald Goertzel's algorithm is a unique Fourier related transform that identifies tonal properties by quantifying resonance in a set of second order IIR filters with direct-form structure.
It is computationally more efficient than typical DFT or FFT algorithms, and yields decent spectral resolution.
In this variation of the algorithm, data is first passed through a 2 pole high pass filter to attenuate spectral dilation, then passed through a Hamming Window to tidy up the frequency range.
The clean windowed data is then passed through a recursive resonance loop over the frequency block to calculate filter coefficients, which are then used to identify real and imaginary magnitude components.
From there, the magnitude components are used to calculate cyclic power.
The power outputs of each period are then compared for dominant cycle estimation, which is plotted over the gradient.
The dominant cycle can also be optionally smoothed or halved based on your preferences.
Bar colors are included in this script. The color scheme is a gradient based on dominant cycle momentum.
Signals and alert conditions are included in this script as well, and can be customized to your liking.
The two main signal types in this script are:
-> Dominant Cycle - Signals based on dominant cycle or half dominant cycle changes from positive to negative strength or vice versa.
-> Confluence - Signals based on confluence emergence. Based on the majority of measured cycles or all measured cycles showing positive or negative strength.
The signals in this are also externally accessible by other scripts.
The output format is 1 for long signals, and -1 for short signals.
To integrate these signals with your own system, use a source input in your script and assign it to this script's "Direction Signals" output variable from the dropdown tab.
In addition, I included two external output variables that show dominant cycle strength and average cycle strength.
They can be integrated into your own scripts by using a source input and selecting the proper output variable, just like the signals.
The Strength Analyzer is a versatile and powerful analytical tool to have in the arsenal for generating unique insights about momentum and cycle dominance.
By analyzing strength on a spectral basis, we can look at relative price movements on a deeper level and gain insights that aren't necessarily obvious from simply looking at a price chart.
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This is a premium script, and access is provided on an invite-only basis.
To gain access, get a copy of the script overview, or for any other inquiries, send me a direct message!
I look forward to hearing from you!
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General Disclaimer:
Trading stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument has large potential rewards, but also large potential risk.
You must be aware of the risks and be willing to accept them in order to invest in stocks, futures, Forex, options, ETFs or cryptocurrencies.
Don’t trade with money you can’t afford to lose.
This is neither a solicitation nor an offer to Buy/Sell stocks, futures, Forex, options, ETFs, cryptocurrencies or any other financial instrument.
No representation is being made that any account will or is likely to achieve profits or losses of any kind.
The past performance of any trading system or methodology is not necessarily indicative of future results.
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Note:
Because TV's UI can't handle displaying style options for 43 fills with 42 colors, the color scheme of the analyzer is currently not editable.
However, no other sacrifices to functionality or quality were made in this project.
As the TV team performs updates on the platform, the ability to customize this color scheme will likely come as well.
Also, it's important to note that this script uses a heavy amount of calculations to generate this output.
At times (very infrequently), TV will throw an error message saying "Calculation Takes Too Long", likely due to a momentary lull in available server space.
If you receive this error, simply hide then unhide the indicator, and everything should function as expected.
Market GloryV1 -Introducing the new Market Glory indicator! In this indicator you will find:
- Dynamic Trends: a beta feature that takes into account both the maximum high and lowest low values anywhere between 5 to 200 bars back to determine the respective resistance and support levels at all times, with a trailing guidance middle bar that can serve as a meter for direction and takes into account only the close values of the defined 5-200 lookback bars! ( ***Strictly based on the 1 minute timeframe. )
- Engulfing bars: a beta feature that allows you to seek out potential reversal bars, based on the dema tema clouds and the respective bar's open and close!!
- Cycle bars: a Market Sniper classic feature, enabling you to catch momentum, consolidation, and continuation via hollow candles! This is achieved by detecting whether the open and close values stem from within the dema tema cloud's boundaries!
- Levels: also a Market Sniper classic, which lets you see support and resistance levels based on previous daily, weekly, and monthly opening and closing values! Also takes into account current closing price action, which will update the levels after being broken!! Furthermore, takes into account fibonacci steps (0.236, 0.382, and 0.5) per timeframe to determine where the nearest level will draw out. **The Calibration feature enables you to look ahead for potential upcoming resistances, with maximum precision.
- EMA crossings: A legacy feature in almost any popular indicator, as a means to correspond with the dema tema cycles for better entries and exits!!
- Multi-timeframe popup labels: By hovering (or long pressing in mobile) over the support and resistance level labels, you can see each dedicated timeframe's current cycle and crossing, to assess whether the stock is following a particular direction! (based solely on real-time close value)
- Lastly...
--- Fully customizable options in coloring and values, including ready-to-go defaults with tooltips to guide you to the Glory you deserve!!!
Cyclical IndicatorThis tool is an oscillator that detects cycles.
It is built on the basis of our centered moving averages.
It is fully configurable in design moreover it is possible to set the centering through the offset !
Offset 2, half cycle centering.
Offset 4, 1/4 cycle centering.
Recommended setting :
Offset 4
Cyclical ratio 2
200WMA Overlay + Z (heatmap mapping)This script enhances the classic 200-week moving average (200WMA), a long-term market reference line, by adding Z-Score mapping and optional helper bands for extended cycle analysis.
Features
200WMA Anchor: Plots the true 200-week simple moving average on any chart, a widely followed metric for long-term Bitcoin and crypto cycles.
Helper Multiples: Optional overlay of key historical ratios (×0.625, ×1.6, ×2.0, ×2.5) often referenced as cycle support/resistance zones.
Z-Score Mapping: Translates the ratio of price to 200WMA into a Z-Score scale (from +2.5 to –2.5), offering a statistical perspective on whether the market is undervalued, neutral, or overheated relative to its long-term mean.
On-Chart Label: Current Z-Score displayed directly on the last bar for quick reference.
How to Use
Long-Term Valuation: The 200WMA serves as a “fair value” baseline; large deviations highlight extended phases of market sentiment.
Heatmap Context:
Positive Z values typically mark undervaluation or favorable accumulation zones.
Negative Z values highlight overvaluation or profit-taking / distribution zones.
Strategic View: Best used to contextualize long-term market cycles, not for short-term signals.
Confluence Approach: This indicator should not be used alone — combine it with other technical or fundamental tools for stronger decision-making.
Originality
Unlike a basic 200WMA overlay, this version:
Incorporates multi-band ratios for extended cycle mapping.
Introduces a custom Z-Score scale tied directly to price/WMA ratios.
Provides both visual structure and statistical interpretation on a single overlay.
Hellenic EMA Matrix - Α Ω PremiumHellenic EMA Matrix - Alpha Omega Premium
Complete User Guide
Table of Contents
Introduction
Indicator Philosophy
Mathematical Constants
EMA Types
Settings
Trading Signals
Visualization
Usage Strategies
FAQ
Introduction
Hellenic EMA Matrix is a premium indicator based on mathematical constants of nature: Phi (Phi - Golden Ratio), Pi (Pi), e (Euler's number). The indicator uses these universal constants to create dynamic EMAs that adapt to the natural rhythms of the market.
Key Features:
6 EMA types based on mathematical constants
Premium visualization with Neon Glow and Gradient Clouds
Automatic Fast/Mid/Slow EMA sorting
STRONG signals for powerful trends
Pulsing Ribbon Bar for instant trend assessment
Works on all timeframes (M1 - MN)
Indicator Philosophy
Why Mathematical Constants?
Traditional EMAs use arbitrary periods (9, 21, 50, 200). Hellenic Matrix goes further, using universal mathematical constants found in nature:
Phi (1.618) - Golden Ratio: galaxy spirals, seashells, human body proportions
Pi (3.14159) - Pi: circles, waves, cycles
e (2.71828) - Natural logarithm base: exponential growth, radioactive decay
Markets are also a natural system composed of millions of participants. Using mathematical constants allows tuning into the natural rhythms of market cycles.
Mathematical Constants
Phi (Phi) - Golden Ratio
Phi = 1.618033988749895
Properties:
Phi² = Phi + 1 = 2.618
Phi³ = 4.236
Phi⁴ = 6.854
Application: Ideal for trending movements and Fibonacci corrections
Pi (Pi) - Pi Number
Pi = 3.141592653589793
Properties:
2Pi = 6.283 (full circle)
3Pi = 9.425
4Pi = 12.566
Application: Excellent for cyclical markets and wave structures
e (Euler) - Euler's Number
e = 2.718281828459045
Properties:
e² = 7.389
e³ = 20.085
e⁴ = 54.598
Application: Suitable for exponential movements and volatile markets
EMA Types
1. Phi (Phi) - Golden Ratio EMA
Description: EMA based on the golden ratio
Period Formula:
Period = Phi^n × Base Multiplier
Parameters:
Phi Power Level (1-8): Power of Phi
Phi¹ = 1.618 → ~16 period (with Base=10)
Phi² = 2.618 → ~26 period
Phi³ = 4.236 → ~42 period (recommended)
Phi⁴ = 6.854 → ~69 period
Recommendations:
Phi² or Phi³ for day trading
Phi⁴ or Phi⁵ for swing trading
Works excellently as Fast EMA
2. Pi (Pi) - Circular EMA
Description: EMA based on Pi for cyclical movements
Period Formula:
Period = Pi × Multiple × Base Multiplier
Parameters:
Pi Multiple (1-10): Pi multiplier
1Pi = 3.14 → ~31 period (with Base=10)
2Pi = 6.28 → ~63 period (recommended)
3Pi = 9.42 → ~94 period
Recommendations:
2Pi ideal as Mid or Slow EMA
Excellently identifies cycles and waves
Use on volatile markets (crypto, forex)
3. e (Euler) - Natural EMA
Description: EMA based on natural logarithm
Period Formula:
Period = e^n × Base Multiplier
Parameters:
e Power Level (1-6): Power of e
e¹ = 2.718 → ~27 period (with Base=10)
e² = 7.389 → ~74 period (recommended)
e³ = 20.085 → ~201 period
Recommendations:
e² works excellently as Slow EMA
Ideal for stocks and indices
Filters noise well on lower timeframes
4. Delta (Delta) - Adaptive EMA
Description: Adaptive EMA that changes period based on volatility
Period Formula:
Period = Base Period × (1 + (Volatility - 1) × Factor)
Parameters:
Delta Base Period (5-200): Base period (default 20)
Delta Volatility Sensitivity (0.5-5.0): Volatility sensitivity (default 2.0)
How it works:
During low volatility → period decreases → EMA reacts faster
During high volatility → period increases → EMA smooths noise
Recommendations:
Works excellently on news and sharp movements
Use as Fast EMA for quick adaptation
Sensitivity 2.0-3.0 for crypto, 1.0-2.0 for stocks
5. Sigma (Sigma) - Composite EMA
Description: Composite EMA combining multiple active EMAs
Composition Methods:
Weighted Average (default):
Sigma = (Phi + Pi + e + Delta) / 4
Simple average of all active EMAs
Geometric Mean:
Sigma = fourth_root(Phi × Pi × e × Delta)
Geometric mean (more conservative)
Harmonic Mean:
Sigma = 4 / (1/Phi + 1/Pi + 1/e + 1/Delta)
Harmonic mean (more weight to smaller values)
Recommendations:
Enable for additional confirmation
Use as Mid EMA
Weighted Average - most universal method
6. Lambda (Lambda) - Wave EMA
Description: Wave EMA with sinusoidal period modulation
Period Formula:
Period = Base Period × (1 + Amplitude × sin(2Pi × bar / Frequency))
Parameters:
Lambda Base Period (10-200): Base period
Lambda Wave Amplitude (0.1-2.0): Wave amplitude
Lambda Wave Frequency (10-200): Wave frequency in bars
How it works:
Period pulsates sinusoidally
Creates wave effect following market cycles
Recommendations:
Experimental EMA for advanced users
Works well on cyclical markets
Frequency = 50 for day trading, 100+ for swing
Settings
Matrix Core Settings
Base Multiplier (1-100)
Multiplies all EMA periods
Base = 1: Very fast EMAs (Phi³ = 4, 2Pi = 6, e² = 7)
Base = 10: Standard (Phi³ = 42, 2Pi = 63, e² = 74)
Base = 20: Slow EMAs (Phi³ = 85, 2Pi = 126, e² = 148)
Recommendations by timeframe:
M1-M5: Base = 5-10
M15-H1: Base = 10-15 (recommended)
H4-D1: Base = 15-25
W1-MN: Base = 25-50
Matrix Source
Data source selection for EMA calculation:
close - closing price (standard)
open - opening price
high - high
low - low
hl2 - (high + low) / 2
hlc3 - (high + low + close) / 3
ohlc4 - (open + high + low + close) / 4
When to change:
hlc3 or ohlc4 for smoother signals
high for aggressive longs
low for aggressive shorts
Manual EMA Selection
Critically important setting! Determines which EMAs are used for signal generation.
Use Manual Fast/Slow/Mid Selection
Enabled (default): You select EMAs manually
Disabled: Automatic selection by periods
Fast EMA
Fast EMA - reacts first to price changes
Recommendations:
Phi Golden (recommended) - universal choice
Delta Adaptive - for volatile markets
Must be fastest (smallest period)
Slow EMA
Slow EMA - determines main trend
Recommendations:
Pi Circular (recommended) - excellent trend filter
e Natural - for smoother trend
Must be slowest (largest period)
Mid EMA
Mid EMA - additional signal filter
Recommendations:
e Natural (recommended) - excellent middle level
Pi Circular - alternative
None - for more frequent signals (only 2 EMAs)
IMPORTANT: The indicator automatically sorts selected EMAs by their actual periods:
Fast = EMA with smallest period
Mid = EMA with middle period
Slow = EMA with largest period
Therefore, you can select any combination - the indicator will arrange them correctly!
Premium Visualization
Neon Glow
Enable Neon Glow for EMAs - adds glowing effect around EMA lines
Glow Strength:
Light - subtle glow
Medium (recommended) - optimal balance
Strong - bright glow (may be too bright)
Effect: 2 glow layers around each EMA for 3D effect
Gradient Clouds
Enable Gradient Clouds - fills space between EMAs with gradient
Parameters:
Cloud Transparency (85-98): Cloud transparency
95-97 (recommended)
Higher = more transparent
Dynamic Cloud Intensity - automatically changes transparency based on EMA distance
Cloud Colors:
Phi-Pi Cloud:
Blue - when Pi above Phi (bullish)
Gold - when Phi above Pi (bearish)
Pi-e Cloud:
Green - when e above Pi (bullish)
Blue - when Pi above e (bearish)
2 layers for volumetric effect
Pulsing Ribbon Bar
Enable Pulsing Indicator Bar - pulsing strip at bottom/top of chart
Parameters:
Ribbon Position: Top / Bottom (recommended)
Pulse Speed: Slow / Medium (recommended) / Fast
Symbols and colors:
Green filled square - STRONG BULLISH
Pink filled square - STRONG BEARISH
Blue hollow square - Bullish (regular)
Red hollow square - Bearish (regular)
Purple rectangle - Neutral
Effect: Pulsation with sinusoid for living market feel
Signal Bar Highlights
Enable Signal Bar Highlights - highlights bars with signals
Parameters:
Highlight Transparency (88-96): Highlight transparency
Highlight Style:
Light Fill (recommended) - bar background fill
Thin Line - bar outline only
Highlights:
Golden Cross - green
Death Cross - pink
STRONG BUY - green
STRONG SELL - pink
Show Greek Labels
Shows Greek alphabet letters on last bar:
Phi - Phi EMA (gold)
Pi - Pi EMA (blue)
e - Euler EMA (green)
Delta - Delta EMA (purple)
Sigma - Sigma EMA (pink)
When to use: For education or presentations
Show Old Background
Old background style (not recommended):
Green background - STRONG BULLISH
Pink background - STRONG BEARISH
Blue background - Bullish
Red background - Bearish
Not recommended - use new Gradient Clouds and Pulsing Bar
Info Table
Show Info Table - table with indicator information
Parameters:
Position: Top Left / Top Right (recommended) / Bottom Left / Bottom Right
Size: Tiny / Small (recommended) / Normal / Large
Table contents:
EMA list - periods and current values of all active EMAs
Effects - active visual effects
TREND - current trend state:
STRONG UP - strong bullish
STRONG DOWN - strong bearish
Bullish - regular bullish
Bearish - regular bearish
Neutral - neutral
Momentum % - percentage deviation of price from Fast EMA
Setup - current Fast/Slow/Mid configuration
Trading Signals
Show Golden/Death Cross
Golden Cross - Fast EMA crosses Slow EMA from below (bullish signal) Death Cross - Fast EMA crosses Slow EMA from above (bearish signal)
Symbols:
Yellow dot "GC" below - Golden Cross
Dark red dot "DC" above - Death Cross
Show STRONG Signals
STRONG BUY and STRONG SELL - the most powerful indicator signals
Conditions for STRONG BULLISH:
EMA Alignment: Fast > Mid > Slow (all EMAs aligned)
Trend: Fast > Slow (clear uptrend)
Distance: EMAs separated by minimum 0.15%
Price Position: Price above Fast EMA
Fast Slope: Fast EMA rising
Slow Slope: Slow EMA rising
Mid Trending: Mid EMA also rising (if enabled)
Conditions for STRONG BEARISH:
Same but in reverse
Visual display:
Green label "STRONG BUY" below bar
Pink label "STRONG SELL" above bar
Difference from Golden/Death Cross:
Golden/Death Cross = crossing moment (1 bar)
STRONG signal = sustained trend (lasts several bars)
IMPORTANT: After fixes, STRONG signals now:
Work on all timeframes (M1 to MN)
Don't break on small retracements
Work with any Fast/Mid/Slow combination
Automatically adapt thanks to EMA sorting
Show Stop Loss/Take Profit
Automatic SL/TP level calculation on STRONG signal
Parameters:
Stop Loss (ATR) (0.5-5.0): ATR multiplier for stop loss
1.5 (recommended) - standard
1.0 - tight stop
2.0-3.0 - wide stop
Take Profit R:R (1.0-5.0): Risk/reward ratio
2.0 (recommended) - standard (risk 1.5 ATR, profit 3.0 ATR)
1.5 - conservative
3.0-5.0 - aggressive
Formulas:
LONG:
Stop Loss = Entry - (ATR × Stop Loss ATR)
Take Profit = Entry + (ATR × Stop Loss ATR × Take Profit R:R)
SHORT:
Stop Loss = Entry + (ATR × Stop Loss ATR)
Take Profit = Entry - (ATR × Stop Loss ATR × Take Profit R:R)
Visualization:
Red X - Stop Loss
Green X - Take Profit
Levels remain active while STRONG signal persists
Trading Signals
Signal Types
1. Golden Cross
Description: Fast EMA crosses Slow EMA from below
Signal: Beginning of bullish trend
How to trade:
ENTRY: On bar close with Golden Cross
STOP: Below local low or below Slow EMA
TARGET: Next resistance level or 2:1 R:R
Strengths:
Simple and clear
Works well on trending markets
Clear entry point
Weaknesses:
Lags (signal after movement starts)
Many false signals in ranging markets
May be late on fast moves
Optimal timeframes: H1, H4, D1
2. Death Cross
Description: Fast EMA crosses Slow EMA from above
Signal: Beginning of bearish trend
How to trade:
ENTRY: On bar close with Death Cross
STOP: Above local high or above Slow EMA
TARGET: Next support level or 2:1 R:R
Application: Mirror of Golden Cross
3. STRONG BUY
Description: All EMAs aligned + trend + all EMAs rising
Signal: Powerful bullish trend
How to trade:
ENTRY: On bar close with STRONG BUY or on pullback to Fast EMA
STOP: Below Fast EMA or automatic SL (if enabled)
TARGET: Automatic TP (if enabled) or by levels
TRAILING: Follow Fast EMA
Entry strategies:
Aggressive: Enter immediately on signal
Conservative: Wait for pullback to Fast EMA, then enter on bounce
Pyramiding: Add positions on pullbacks to Mid EMA
Position management:
Hold while STRONG signal active
Exit on STRONG SELL or Death Cross appearance
Move stop behind Fast EMA
Strengths:
Most reliable indicator signal
Doesn't break on pullbacks
Catches large moves
Works on all timeframes
Weaknesses:
Appears less frequently than other signals
Requires confirmation (multiple conditions)
Optimal timeframes: All (M5 - D1)
4. STRONG SELL
Description: All EMAs aligned down + downtrend + all EMAs falling
Signal: Powerful bearish trend
How to trade: Mirror of STRONG BUY
Visual Signals
Pulsing Ribbon Bar
Quick market assessment at a glance:
Symbol Color State
Filled square Green STRONG BULLISH
Filled square Pink STRONG BEARISH
Hollow square Blue Bullish
Hollow square Red Bearish
Rectangle Purple Neutral
Pulsation: Sinusoidal, creates living effect
Signal Bar Highlights
Bars with signals are highlighted:
Green highlight: STRONG BUY or Golden Cross
Pink highlight: STRONG SELL or Death Cross
Gradient Clouds
Colored space between EMAs shows trend strength:
Wide clouds - strong trend
Narrow clouds - weak trend or consolidation
Color change - trend change
Info Table
Quick reference in corner:
TREND: Current state (STRONG UP, Bullish, Neutral, Bearish, STRONG DOWN)
Momentum %: Movement strength
Effects: Active visual effects
Setup: Fast/Slow/Mid configuration
Usage Strategies
Strategy 1: "Golden Trailing"
Idea: Follow STRONG signals using Fast EMA as trailing stop
Settings:
Fast: Phi Golden (Phi³)
Mid: Pi Circular (2Pi)
Slow: e Natural (e²)
Base Multiplier: 10
Timeframe: H1, H4
Entry rules:
Wait for STRONG BUY
Enter on bar close or on pullback to Fast EMA
Stop below Fast EMA
Management:
Hold position while STRONG signal active
Move stop behind Fast EMA daily
Exit on STRONG SELL or Death Cross
Take Profit:
Partially close at +2R
Trail remainder until exit signal
For whom: Swing traders, trend followers
Pros:
Catches large moves
Simple rules
Emotionally comfortable
Cons:
Requires patience
Possible extended drawdowns on pullbacks
Strategy 2: "Scalping Bounces"
Idea: Scalp bounces from Fast EMA during STRONG trend
Settings:
Fast: Delta Adaptive (Base 15, Sensitivity 2.0)
Mid: Phi Golden (Phi²)
Slow: Pi Circular (2Pi)
Base Multiplier: 5
Timeframe: M5, M15
Entry rules:
STRONG signal must be active
Wait for price pullback to Fast EMA
Enter on bounce (candle closes above/below Fast EMA)
Stop behind local extreme (15-20 pips)
Take Profit:
+1.5R or to Mid EMA
Or to next level
For whom: Active day traders
Pros:
Many signals
Clear entry point
Quick profits
Cons:
Requires constant monitoring
Not all bounces work
Requires discipline for frequent trading
Strategy 3: "Triple Filter"
Idea: Enter only when all 3 EMAs and price perfectly aligned
Settings:
Fast: Phi Golden (Phi³)
Mid: e Natural (e²)
Slow: Pi Circular (3Pi)
Base Multiplier: 15
Timeframe: H4, D1
Entry rules (LONG):
STRONG BUY active
Price above all three EMAs
Fast > Mid > Slow (all aligned)
All EMAs rising (slope up)
Gradient Clouds wide and bright
Entry:
On bar close meeting all conditions
Or on next pullback to Fast EMA
Stop:
Below Mid EMA or -1.5 ATR
Take Profit:
First target: +3R
Second target: next major level
Trailing: Mid EMA
For whom: Conservative swing traders, investors
Pros:
Very reliable signals
Minimum false entries
Large profit potential
Cons:
Rare signals (2-5 per month)
Requires patience
Strategy 4: "Adaptive Scalper"
Idea: Use only Delta Adaptive EMA for quick volatility reaction
Settings:
Fast: Delta Adaptive (Base 10, Sensitivity 3.0)
Mid: None
Slow: Delta Adaptive (Base 30, Sensitivity 2.0)
Base Multiplier: 3
Timeframe: M1, M5
Feature: Two different Delta EMAs with different settings
Entry rules:
Golden Cross between two Delta EMAs
Both Delta EMAs must be rising/falling
Enter on next bar
Stop:
10-15 pips or below Slow Delta EMA
Take Profit:
+1R to +2R
Or Death Cross
For whom: Scalpers on cryptocurrencies and forex
Pros:
Instant volatility adaptation
Many signals on volatile markets
Quick results
Cons:
Much noise on calm markets
Requires fast execution
High commissions may eat profits
Strategy 5: "Cyclical Trader"
Idea: Use Pi and Lambda for trading cyclical markets
Settings:
Fast: Pi Circular (1Pi)
Mid: Lambda Wave (Base 30, Amplitude 0.5, Frequency 50)
Slow: Pi Circular (3Pi)
Base Multiplier: 10
Timeframe: H1, H4
Entry rules:
STRONG signal active
Lambda Wave EMA synchronized with trend
Enter on bounce from Lambda Wave
For whom: Traders of cyclical assets (some altcoins, commodities)
Pros:
Catches cyclical movements
Lambda Wave provides additional entry points
Cons:
More complex to configure
Not for all markets
Lambda Wave may give false signals
Strategy 6: "Multi-Timeframe Confirmation"
Idea: Use multiple timeframes for confirmation
Scheme:
Higher TF (D1): Determine trend direction (STRONG signal)
Middle TF (H4): Wait for STRONG signal in same direction
Lower TF (M15): Look for entry point (Golden Cross or bounce from Fast EMA)
Settings for all TFs:
Fast: Phi Golden (Phi³)
Mid: e Natural (e²)
Slow: Pi Circular (2Pi)
Base Multiplier: 10
Rules:
All 3 TFs must show one trend
Entry on lower TF
Stop by lower TF
Target by higher TF
For whom: Serious traders and investors
Pros:
Maximum reliability
Large profit targets
Minimum false signals
Cons:
Rare setups
Requires analysis of multiple charts
Experience needed
Practical Tips
DOs
Use STRONG signals as primary - they're most reliable
Let signals develop - don't exit on first pullback
Use trailing stop - follow Fast EMA
Combine with levels - S/R, Fibonacci, volumes
Test on demo before real
Adjust Base Multiplier for your timeframe
Enable visual effects - they help see the picture
Use Info Table - quick situation assessment
Watch Pulsing Bar - instant state indicator
Trust auto-sorting of Fast/Mid/Slow
DON'Ts
Don't trade against STRONG signal - trend is your friend
Don't ignore Mid EMA - it adds reliability
Don't use too small Base Multiplier on higher TFs
Don't enter on Golden Cross in range - check for trend
Don't change settings during open position
Don't forget risk management - 1-2% per trade
Don't trade all signals in row - choose best ones
Don't use indicator in isolation - combine with Price Action
Don't set too tight stops - let trade breathe
Don't over-optimize - simplicity = reliability
Optimal Settings by Asset
US Stocks (SPY, AAPL, TSLA)
Recommendation:
Fast: Phi Golden (Phi³)
Mid: e Natural (e²)
Slow: Pi Circular (2Pi)
Base: 10-15
Timeframe: H4, D1
Features:
Use on daily for swing
STRONG signals very reliable
Works well on trending stocks
Forex (EUR/USD, GBP/USD)
Recommendation:
Fast: Delta Adaptive (Base 15, Sens 2.0)
Mid: Phi Golden (Phi²)
Slow: Pi Circular (2Pi)
Base: 8-12
Timeframe: M15, H1, H4
Features:
Delta Adaptive works excellently on news
Many signals on M15-H1
Consider spreads
Cryptocurrencies (BTC, ETH, altcoins)
Recommendation:
Fast: Delta Adaptive (Base 10, Sens 3.0)
Mid: Pi Circular (2Pi)
Slow: e Natural (e²)
Base: 5-10
Timeframe: M5, M15, H1
Features:
High volatility - adaptation needed
STRONG signals can last days
Be careful with scalping on M1-M5
Commodities (Gold, Oil)
Recommendation:
Fast: Pi Circular (1Pi)
Mid: Phi Golden (Phi³)
Slow: Pi Circular (3Pi)
Base: 12-18
Timeframe: H4, D1
Features:
Pi works excellently on cyclical commodities
Gold responds especially well to Phi
Oil volatile - use wide stops
Indices (S&P500, Nasdaq, DAX)
Recommendation:
Fast: Phi Golden (Phi³)
Mid: e Natural (e²)
Slow: Pi Circular (2Pi)
Base: 15-20
Timeframe: H4, D1, W1
Features:
Very trending instruments
STRONG signals last weeks
Good for position trading
Alerts
The indicator supports 6 alert types:
1. Golden Cross
Message: "Hellenic Matrix: GOLDEN CROSS - Fast EMA crossed above Slow EMA - Bullish trend starting!"
When: Fast EMA crosses Slow EMA from below
2. Death Cross
Message: "Hellenic Matrix: DEATH CROSS - Fast EMA crossed below Slow EMA - Bearish trend starting!"
When: Fast EMA crosses Slow EMA from above
3. STRONG BULLISH
Message: "Hellenic Matrix: STRONG BULLISH SIGNAL - All EMAs aligned for powerful uptrend!"
When: All conditions for STRONG BUY met (first bar)
4. STRONG BEARISH
Message: "Hellenic Matrix: STRONG BEARISH SIGNAL - All EMAs aligned for powerful downtrend!"
When: All conditions for STRONG SELL met (first bar)
5. Bullish Ribbon
Message: "Hellenic Matrix: BULLISH RIBBON - EMAs aligned for uptrend"
When: EMAs aligned bullish + price above Fast EMA (less strict condition)
6. Bearish Ribbon
Message: "Hellenic Matrix: BEARISH RIBBON - EMAs aligned for downtrend"
When: EMAs aligned bearish + price below Fast EMA (less strict condition)
How to Set Up Alerts:
Open indicator on chart
Click on three dots next to indicator name
Select "Create Alert"
In "Condition" field select needed alert:
Golden Cross
Death Cross
STRONG BULLISH
STRONG BEARISH
Bullish Ribbon
Bearish Ribbon
Configure notification method:
Pop-up in browser
Email
SMS (in Premium accounts)
Push notifications in mobile app
Webhook (for automation)
Select frequency:
Once Per Bar Close (recommended) - once on bar close
Once Per Bar - during bar formation
Only Once - only first time
Click "Create"
Tip: Create separate alerts for different timeframes and instruments
FAQ
1. Why don't STRONG signals appear?
Possible reasons:
Incorrect Fast/Mid/Slow order
Solution: Indicator automatically sorts EMAs by periods, but ensure selected EMAs have different periods
Base Multiplier too large
Solution: Reduce Base to 5-10 on lower timeframes
Market in range
Solution: STRONG signals appear only in trends - this is normal
Too strict EMA settings
Solution: Try classic combination: Phi³ / Pi×2 / e² with Base=10
Mid EMA too close to Fast or Slow
Solution: Select Mid EMA with period between Fast and Slow
2. How often should STRONG signals appear?
Normal frequency:
M1-M5: 5-15 signals per day (very active markets)
M15-H1: 2-8 signals per day
H4: 3-10 signals per week
D1: 2-5 signals per month
W1: 2-6 signals per year
If too many signals - market very volatile or Base too small
If too few signals - market in range or Base too large
4. What are the best settings for beginners?
Universal "out of the box" settings:
Matrix Core:
Base Multiplier: 10
Source: close
Phi Golden: Enabled, Power = 3
Pi Circular: Enabled, Multiple = 2
e Natural: Enabled, Power = 2
Delta Adaptive: Enabled, Base = 20, Sensitivity = 2.0
Manual Selection:
Fast: Phi Golden
Mid: e Natural
Slow: Pi Circular
Visualization:
Gradient Clouds: ON
Neon Glow: ON (Medium)
Pulsing Bar: ON (Medium)
Signal Highlights: ON (Light Fill)
Table: ON (Top Right, Small)
Signals:
Golden/Death Cross: ON
STRONG Signals: ON
Stop Loss: OFF (while learning)
Timeframe for learning: H1 or H4
5. Can I use only one EMA?
No, minimum 2 EMAs (Fast and Slow) for signal generation.
Mid EMA is optional:
With Mid EMA = more reliable but rarer signals
Without Mid EMA = more signals but less strict filtering
Recommendation: Start with 3 EMAs (Fast/Mid/Slow), then experiment
6. Does the indicator work on cryptocurrencies?
Yes, works excellently! Especially good on:
Bitcoin (BTC)
Ethereum (ETH)
Major altcoins (SOL, BNB, XRP)
Recommended settings for crypto:
Fast: Delta Adaptive (Base 10-15, Sensitivity 2.5-3.0)
Mid: Pi Circular (2Pi)
Slow: e Natural (e²)
Base: 5-10
Timeframe: M15, H1, H4
Crypto market features:
High volatility → use Delta Adaptive
24/7 trading → set alerts
Sharp movements → wide stops
7. Can I trade only with this indicator?
Technically yes, but NOT recommended.
Best approach - combine with:
Price Action - support/resistance levels, candle patterns
Volume - movement strength confirmation
Fibonacci - retracement and extension levels
RSI/MACD - divergences and overbought/oversold
Fundamental analysis - news, company reports
Hellenic Matrix:
Excellently determines trend and its strength
Provides clear entry/exit points
Doesn't consider fundamentals
Doesn't see major levels
8. Why do Gradient Clouds change color?
Color depends on EMA order:
Phi-Pi Cloud:
Blue - Pi EMA above Phi EMA (bullish alignment)
Gold - Phi EMA above Pi EMA (bearish alignment)
Pi-e Cloud:
Green - e EMA above Pi EMA (bullish alignment)
Blue - Pi EMA above e EMA (bearish alignment)
Color change = EMA order change = possible trend change
9. What is Momentum % in the table?
Momentum % = percentage deviation of price from Fast EMA
Formula:
Momentum = ((Close - Fast EMA) / Fast EMA) × 100
Interpretation:
+0.5% to +2% - normal bullish momentum
+2% to +5% - strong bullish momentum
+5% and above - overheating (correction possible)
-0.5% to -2% - normal bearish momentum
-2% to -5% - strong bearish momentum
-5% and below - oversold (bounce possible)
Usage:
Monitor momentum during STRONG signals
Large momentum = don't enter (wait for pullback)
Small momentum = good entry point
10. How to configure for scalping?
Settings for scalping (M1-M5):
Base Multiplier: 3-5
Source: close or hlc3 (smoother)
Fast: Delta Adaptive (Base 8-12, Sensitivity 3.0)
Mid: None (for more signals)
Slow: Phi Golden (Phi²) or Pi Circular (1Pi)
Visualization:
- Gradient Clouds: ON (helps see strength)
- Neon Glow: OFF (doesn't clutter chart)
- Pulsing Bar: ON (quick assessment)
- Signal Highlights: ON
Signals:
- Golden/Death Cross: ON
- STRONG Signals: ON
- Stop Loss: ON (1.0-1.5 ATR, R:R 1.5-2.0)
Scalping rules:
Trade only STRONG signals
Enter on bounce from Fast EMA
Tight stops (10-20 pips)
Quick take profit (+1R to +2R)
Don't hold through news
11. How to configure for long-term investing?
Settings for investing (D1-W1):
Base Multiplier: 20-30
Source: close
Fast: Phi Golden (Phi³ or Phi⁴)
Mid: e Natural (e²)
Slow: Pi Circular (3Pi or 4Pi)
Visualization:
- Gradient Clouds: ON
- Neon Glow: ON (Medium)
- Everything else - to taste
Signals:
- Golden/Death Cross: ON
- STRONG Signals: ON
- Stop Loss: OFF (use percentage stop)
Investing rules:
Enter only on STRONG signals
Hold while STRONG active (weeks/months)
Stop below Slow EMA or -10%
Take profit: by company targets or +50-100%
Ignore short-term pullbacks
12. What if indicator slows down chart?
Indicator is optimized, but if it slows:
Disable unnecessary visual effects:
Neon Glow: OFF (saves 8 plots)
Gradient Clouds: ON but low quality
Lambda Wave EMA: OFF (if not using)
Reduce number of active EMAs:
Sigma Composite: OFF
Lambda Wave: OFF
Leave only Phi, Pi, e, Delta
Simplify settings:
Pulsing Bar: OFF
Greek Labels: OFF
Info Table: smaller size
13. Can I use on different timeframes simultaneously?
Yes! Multi-timeframe analysis is very powerful:
Classic scheme:
Higher TF (D1, W1) - determine global trend
Wait for STRONG signal
This is our trading direction
Middle TF (H4, H1) - look for confirmation
STRONG signal in same direction
Precise entry zone
Lower TF (M15, M5) - entry point
Golden Cross or bounce from Fast EMA
Precise stop loss
Example:
W1: STRONG BUY active (global uptrend)
H4: STRONG BUY appeared (confirmation)
M15: Wait for Golden Cross or bounce from Fast EMA → ENTRY
Advantages:
Maximum reliability
Clear timeframe hierarchy
Large targets
14. How does indicator work on news?
Delta Adaptive EMA adapts excellently to news:
Before news:
Low volatility → Delta EMA becomes fast → pulls to price
During news:
Sharp volatility spike → Delta EMA slows → filters noise
After news:
Volatility normalizes → Delta EMA returns to normal
Recommendations:
Don't trade at news release moment (spreads widen)
Wait for STRONG signal after news (2-5 bars)
Use Delta Adaptive as Fast EMA for quick reaction
Widen stops by 50-100% during important news
Advanced Techniques
Technique 1: "Divergences with EMA"
Idea: Look for discrepancies between price and Fast EMA
Bullish divergence:
Price makes lower low
Fast EMA makes higher low
= Possible reversal up
Bearish divergence:
Price makes higher high
Fast EMA makes lower high
= Possible reversal down
How to trade:
Find divergence
Wait for STRONG signal in divergence direction
Enter on confirmation
Technique 2: "EMA Tunnel"
Idea: Use space between Fast and Slow EMA as "tunnel"
Rules:
Wide tunnel - strong trend, hold position
Narrow tunnel - weak trend or consolidation, caution
Tunnel narrowing - trend weakening, prepare to exit
Tunnel widening - trend strengthening, can add
Visually: Gradient Clouds show this automatically!
Trading:
Enter on STRONG signal (tunnel starts widening)
Hold while tunnel wide
Exit when tunnel starts narrowing
Technique 3: "Wave Analysis with Lambda"
Idea: Lambda Wave EMA creates sinusoid matching market cycles
Setup:
Lambda Base Period: 30
Lambda Wave Amplitude: 0.5
Lambda Wave Frequency: 50 (adjusted to asset cycle)
How to find correct Frequency:
Look at historical cycles (distance between local highs)
Average distance = your Frequency
Example: if highs every 40-60 bars, set Frequency = 50
Trading:
Enter when Lambda Wave at bottom of sinusoid (growth potential)
Exit when Lambda Wave at top (fall potential)
Combine with STRONG signals
Technique 4: "Cluster Analysis"
Idea: When all EMAs gather in narrow cluster = powerful breakout soon
Cluster signs:
All EMAs (Phi, Pi, e, Delta) within 0.5-1% of each other
Gradient Clouds almost invisible
Price jumping around all EMAs
Trading:
Identify cluster (all EMAs close)
Determine breakout direction (where more volume, higher TFs direction)
Wait for breakout and STRONG signal
Enter on confirmation
Target = cluster size × 3-5
This is very powerful technique for big moves!
Technique 5: "Sigma as Dynamic Level"
Idea: Sigma Composite EMA = average of all EMAs = magnetic level
Usage:
Enable Sigma Composite (Weighted Average)
Sigma works as dynamic support/resistance
Price often returns to Sigma before trend continuation
Trading:
In trend: Enter on bounces from Sigma
In range: Fade moves from Sigma (trade return to Sigma)
On breakout: Sigma becomes support/resistance
Risk Management
Basic Rules
1. Position Size
Conservative: 1% of capital per trade
Moderate: 2% of capital per trade (recommended)
Aggressive: 3-5% (only for experienced)
Calculation formula:
Lot Size = (Capital × Risk%) / (Stop in pips × Pip value)
2. Risk/Reward Ratio
Minimum: 1:1.5
Standard: 1:2 (recommended)
Optimal: 1:3
Aggressive: 1:5+
3. Maximum Drawdown
Daily: -3% to -5%
Weekly: -7% to -10%
Monthly: -15% to -20%
Upon reaching limit → STOP trading until end of period
Position Management Strategies
1. Fixed Stop
Method:
Stop below/above Fast EMA or local extreme
DON'T move stop against position
Can move to breakeven
For whom: Beginners, conservative traders
2. Trailing by Fast EMA
Method:
Each day (or bar) move stop to Fast EMA level
Position closes when price breaks Fast EMA
Advantages:
Stay in trend as long as possible
Automatically exit on reversal
For whom: Trend followers, swing traders
3. Partial Exit
Method:
50% of position close at +2R
50% hold with trailing by Mid EMA or Slow EMA
Advantages:
Lock profit
Leave position for big move
Psychologically comfortable
For whom: Universal method (recommended)
4. Pyramiding
Method:
First entry on STRONG signal (50% of planned position)
Add 25% on pullback to Fast EMA
Add another 25% on pullback to Mid EMA
Overall stop below Slow EMA
Advantages:
Average entry price
Reduce risk
Increase profit in strong trends
Caution:
Works only in trends
In range leads to losses
For whom: Experienced traders
Trading Psychology
Correct Mindset
1. Indicator is a tool, not holy grail
Indicator shows probability, not guarantee
There will be losing trades - this is normal
Important is series statistics, not one trade
2. Trust the system
If STRONG signal appeared - enter
Don't search for "perfect" moment
Follow trading plan
3. Patience
STRONG signals don't appear every day
Better miss signal than enter against trend
Quality over quantity
4. Discipline
Always set stop loss
Don't move stop against position
Don't increase risk after losses
Beginner Mistakes
1. "I know better than indicator"
Indicator says STRONG BUY, but you think "too high, will wait for pullback"
Result: miss profitable move
Solution: Trust signals or don't use indicator
2. "Will reverse now for sure"
Trading against STRONG trend
Result: stops, stops, stops
Solution: Trend is your friend, trade with trend
3. "Will hold a bit more"
Don't exit when STRONG signal disappears
Greed eats profit
Solution: If signal gone - exit!
4. "I'll recover"
After losses double risk
Result: huge losses
Solution: Fixed % risk ALWAYS
5. "I don't like this signal"
Skip signals because of "feeling"
Result: inconsistency, no statistics
Solution: Trade ALL signals or clearly define filters
Trading Journal
What to Record
For each trade:
1. Entry/exit date and time
2. Instrument and timeframe
3. Signal type
Golden Cross
STRONG BUY
STRONG SELL
Death Cross
4. Indicator settings
Fast/Mid/Slow EMA
Base Multiplier
Other parameters
5. Chart screenshot
Entry moment
Exit moment
6. Trade parameters
Position size
Stop loss
Take Profit
R:R
7. Result
Profit/Loss in $
Profit/Loss in %
Profit/Loss in R
8. Notes
What was right
What was wrong
Emotions during trade
Lessons
Journal Analysis
Analyze weekly:
1. Win Rate
Win Rate = (Profitable trades / All trades) × 100%
Good: 50-60%
Excellent: 60-70%
Exceptional: 70%+
2. Average R
Average R = Sum of all R / Number of trades
Good: +0.5R
Excellent: +1.0R
Exceptional: +1.5R+
3. Profit Factor
Profit Factor = Total profit / Total losses
Good: 1.5+
Excellent: 2.0+
Exceptional: 3.0+
4. Maximum Drawdown
Track consecutive losses
If more than 5 in row - stop, check system
5. Best/Worst Trades
What was common in best trades? (do more)
What was common in worst trades? (avoid)
Pre-Trade Checklist
Technical Analysis
STRONG signal active (BUY or SELL)
All EMAs properly aligned (Fast > Mid > Slow or reverse)
Price on correct side of Fast EMA
Gradient Clouds confirm trend
Pulsing Bar shows STRONG state
Momentum % in normal range (not overheated)
No close strong levels against direction
Higher timeframe doesn't contradict
Risk Management
Position size calculated (1-2% risk)
Stop loss set
Take profit calculated (minimum 1:2)
R:R satisfactory
Daily/weekly risk limit not exceeded
No other open correlated positions
Fundamental Analysis
No important news in coming hours
Market session appropriate (liquidity)
No contradicting fundamentals
Understand why asset is moving
Psychology
Calm and thinking clearly
No emotions from previous trades
Ready to accept loss at stop
Following trading plan
Not revenging market for past losses
If at least one point is NO - think twice before entering!
Learning Roadmap
Week 1: Familiarization
Goals:
Install and configure indicator
Study all EMA types
Understand visualization
Tasks:
Add indicator to chart
Test all Fast/Mid/Slow settings
Play with Base Multiplier on different timeframes
Observe Gradient Clouds and Pulsing Bar
Study Info Table
Result: Comfort with indicator interface
Week 2: Signals
Goals:
Learn to recognize all signal types
Understand difference between Golden Cross and STRONG
Tasks:
Find 10 Golden Cross examples in history
Find 10 STRONG BUY examples in history
Compare their results (which worked better)
Set up alerts
Get 5 real alerts
Result: Understanding signals
Week 3: Demo Trading
Goals:
Start trading signals on demo account
Gather statistics
Tasks:
Open demo account
Trade ONLY STRONG signals
Keep journal (minimum 20 trades)
Don't change indicator settings
Strictly follow stop losses
Result: 20+ documented trades
Week 4: Analysis
Goals:
Analyze demo trading results
Optimize approach
Tasks:
Calculate win rate and average R
Find patterns in profitable trades
Find patterns in losing trades
Adjust approach (not indicator!)
Write trading plan
Result: Trading plan on 1 page
Month 2: Improvement
Goals:
Deepen understanding
Add additional techniques
Tasks:
Study multi-timeframe analysis
Test combinations with Price Action
Try advanced techniques (divergences, tunnels)
Continue demo trading (minimum 50 trades)
Achieve stable profitability on demo
Result: Win rate 55%+ and Profit Factor 1.5+
Month 3: Real Trading
Goals:
Transition to real account
Maintain discipline
Tasks:
Open small real account
Trade minimum lots
Strictly follow trading plan
DON'T increase risk
Focus on process, not profit
Result: Psychological comfort on real
Month 4+: Scaling
Goals:
Increase account
Become consistently profitable
Tasks:
With 60%+ win rate can increase risk to 2%
Upon doubling account can add capital
Continue keeping journal
Periodically review and improve strategy
Share experience with community
Result: Stable profitability month after month
Additional Resources
Recommended Reading
Technical Analysis:
"Technical Analysis of Financial Markets" - John Murphy
"Trading in the Zone" - Mark Douglas (psychology)
"Market Wizards" - Jack Schwager (trader interviews)
EMA and Moving Averages:
"Moving Averages 101" - Steve Burns
Articles on Investopedia about EMA
Risk Management:
"The Mathematics of Money Management" - Ralph Vince
"Trade Your Way to Financial Freedom" - Van K. Tharp
Trading Journals:
Edgewonk (paid, very powerful)
Tradervue (free version + premium)
Excel/Google Sheets (free)
Screeners:
TradingView Stock Screener
Finviz (stocks)
CoinMarketCap (crypto)
Conclusion
Hellenic EMA Matrix is a powerful tool based on universal mathematical constants of nature. The indicator combines:
Mathematical elegance - Phi, Pi, e instead of arbitrary numbers
Premium visualization - Neon Glow, Gradient Clouds, Pulsing Bar
Reliable signals - STRONG BUY/SELL work on all timeframes
Flexibility - 6 EMA types, adaptation to any trading style
Automation - auto-sorting EMAs, SL/TP calculation, alerts
Key Success Principles:
Simplicity - start with basic settings (Phi/Pi/e, Base=10)
Discipline - follow STRONG signals strictly
Patience - wait for quality setups
Risk Management - 1-2% per trade, ALWAYS
Journal - document every trade
Learning - constantly improve skills
Remember:
Indicator shows probability, not guarantee
Important is series statistics, not one trade
Psychology more important than technique
Quality more important than quantity
Process more important than result
Acknowledgments
Thank you for using Hellenic EMA Matrix - Alpha Omega Premium!
The indicator was created with love for mathematics, markets, and beautiful visualization.
Wishing you profitable trading!
Guide Version: 1.0
Date: 2025
Compatibility: Pine Script v6, TradingView
"In the simplicity of mathematical constants lies the complexity of market movements"
TDT Candle CounterThis indicator allows you to count candles inside a custom date range and display labels directly on the chart.
It supports three different counting modes:
🔢 Modes
Every Candle → Marks every bar sequentially (1, 2, 3, 4, …).
Alternative Sequence → Marks bars that match the sequence 1, 5, 9, 17, 25, 37, ….
Special Sequence (default) → Marks bars that match the sequence 1, 3, 7, 13, 21, 31, ….
Each mode has its own color so you can quickly distinguish which cycle is active.
⚙️ Features
Custom start and end date for the counting period.
Option to highlight the active period with a background color.
Labels are positioned above or below candles depending on the initial direction.
Alerts when:
Counting starts
Counting ends
🎯 Use Cases
Visualize candle sequences for cycle analysis.
Track market structure with custom numerical references.
Combine with other tools to study periodic behavior.
Inspired by Time Dilation Theory (TDT)
This counting approach is inspired by the Time Dilation Theory (TDT) methodology created by ICT Morpheus. According to TDT, markets unfold in cycles of 1, 3, 7, 13, 21… etc., reflecting natural rhythms of expansion, contraction, and distortion—an idea grounded in fractal time behavior across multi-timeframe analysis
Incorporating TDT principles into this tool helps visualize and align potential turning points and momentum shifts across different timeframes.
Inter Cycle Valuation | QuantumResearchIntroducing Inter Cycle Valuation by QuantumResearch
A Multi-Factor Adaptive Z-Score System for Market Valuation & Reversal Potential
🧠 Overview
The Inter Cycle Valuation System is a sophisticated multi-factor indicator designed to evaluate the market’s cyclical valuation zones using a blend of momentum, volatility, mean-reversion, and risk-based metrics. It delivers a unified Z-Score—ranging from extremely oversold to overheated conditions—empowering traders to identify high-probability market turning points.
Rather than relying on a single indicator, Inter Cycle blends over 15 diverse Z-score factors, including RSI, ROC, VWAP deviation, Repulse, PGO, and statistical ratios like Sharpe, Sortino, and Omega. This multi-dimensional view allows traders to assess market extremes with greater confidence.
🧩 1. Key Features
📌 Multi-Factor Z-Score System
Inter Cycle integrates 16+ unique indicators into a single composite score. Each input is normalized via a Z-score to ensure balance and reduce bias, helping prevent outlier distortion.
⚙️ Indicator Diversity
Momentum: RSI, ROC, Chande Momentum, Repulse
Mean Reversion: VWAP deviation, Median rank, PGO
Volatility: BB% positioning, Intraday Momentum Index
Risk Ratios: Sharpe, Sortino, Omega
Fractal Geometry: Crosby Ratio
📈 Visually Intuitive Output
Gradient-based area plot for valuation intensity
Optional background heatmap for oversold/overbought zones
Table displaying real-time Z-score values for each component
Dynamic market suggestions: Accumulate, Do Nothing, or Distribute
📊 On-Chart Dashboard
The valuation dashboard displays key stats like Z-price, Z-rsi, Z-mfi, Z-roc, Z-crosby, and more—allowing for real-time interpretation without leaving the chart.
🔍 2. How It Works
1️⃣ Z-Score Normalization
Each indicator is transformed into a Z-score to standardize the values. This ensures that one factor does not dominate due to its scale or volatility.
2️⃣ Multi-Factor Aggregation
All Z-scores are averaged into a single score—called the "Inter Cycle Score"—giving you a reliable snapshot of market positioning.
3️⃣ Actionable Thresholds
🟩 Below -1.6 → “Accumulate Aggressively”
🟨 Between -1.5 and -0.65 → “Accumulate”
⚪ Between -0.5 and +0.5 → “Do Nothing”
🟧 Above +1.2 → “Distribute”
🟥 Above +1.55 → “Distribute Aggressively”
The system prints these labels automatically in real time.
📌 3. Valuation Zones
📉 Strongly Undervalued (< -1.6) → Prime accumulation
📉 Moderately Undervalued (-1.5 to -0.65) → Cautious entries
⚖️ Neutral/Fair (-0.5 to +0.5) → Wait-and-see
📈 Moderately Overheated (+1.2 to +1.55) → Begin reducing risk
🔥 Strongly Overheated (> +1.55) → Take profits, reduce exposure
This structure helps traders and investors clearly interpret current market cycles and position accordingly.
🔁 4. Use Cases & Applications
🔁 Cycle-Based Market Rotation
Great for timing market rotations by spotting macro tops and bottoms. Use the valuation dashboard to rotate capital across assets at optimal phases.
📈 Mean Reversion Entry Triggers
Z-Score combinations such as VWAP deviation + RSI + ROC help pinpoint high-probability mean reversion setups.
📉 Risk-Based Trend Exhaustion
With integrated Sharpe, Sortino, and Omega ratios, you can identify unsustainable moves fueled by low-quality momentum.
💼 Swing Trading & Portfolio Rebalancing
The Inter Cycle score can be used as a filter for swing setups or to rebalance holdings when conditions become extreme.
✅ Conclusion
Inter Cycle Valuation by QuantumResearch is a precision tool for any trader or investor seeking structured insights into market cycles. With its blend of valuation, risk, momentum, and reversion components—standardized via Z-scores—it offers a high-level framework to identify when markets are overheated or undervalued.
Who Should Use It?
✅ Swing Traders & Medium-Term Investors
✅ Portfolio Managers looking for capital rotation signals
✅ Quant Traders and Stat Arb enthusiasts
✅ Macro Traders monitoring cyclical inflection zones
⚠️ Disclaimer
The content provided by this indicator is for educational and informational purposes only. Nothing herein constitutes financial or investment advice. Trading and investing involve risk, including the potential loss of capital. Always backtest and apply risk management suited to your strategy.
OmniPulse (Fixed Version)OmniPulse (Fixed Version) – Description
OmniPulse is a multi-indicator framework designed to combine three core oscillators—RSI, Stochastic, and Momentum—at various lookback lengths, then refine their signals using placeholder features such as machine learning forecasting, adaptive cycle detection, and neural network filtering. While some of these advanced features are not natively supported in Pine Script, they are represented here in simplified forms to illustrate how a more sophisticated system could be structured.
Key Components:
Multi-Length Oscillator Arrays
RSI (calcrsi() function)
Stochastic (placeholder via ta.sma() on a typical price average)
Momentum (ta.roc())
These are calculated for multiple lengths defined by the rsiLengths, stochLengths, and momentumLengths arrays.
Dual-Threshold Convergence
Compares each oscillator’s value to user-defined upper/lower thresholds (threshold1, threshold2) to identify bullish or bearish conditions.
Summarizes results in a convergence score.
Placeholder Machine Learning Forecast
Demonstrates a simple averaging of oscillator values as a “forecast” when toggled on.
Adaptive Cycle Detection (Placeholder)
Introduces a static cycle period (e.g., 20.0) as a placeholder for more advanced transforms.
Neural Network Filter (Placeholder)
Averages convergence, forecast, and cyclePeriod into a single filteredSignal.
Signal Plotting
Plots the filtered signal on the chart.
Highlights potential bullish or bearish extremes with shape markers based on percentile thresholds.
Practical Use & Extension:
Real Multi-Timeframe Analysis: Replace placeholders with request.security() for each timeframe.
Advanced Forecasting: Incorporate custom or external machine learning models.
Genuine Cycle Detection: Implement more sophisticated logic or user-defined cycle detection tools.
Neural Network Heuristics: Expand the placeholder step into a deeper filtering or weighting system.
Overall, OmniPulse serves as an adaptable blueprint for traders and developers, showcasing how multiple indicators and advanced concepts might be combined into a cohesive, signal-generating framework.
Bitcoin CycleThis script displays 4 different Moving Averages:
2 Year Moving Average (White)
1 Year Moving Average (Doubled in value, Red)
116 Day Moving Average (Transparent, Red)
232 Day Moving Average (Transparent, White)
For the last cycles: once the 2 year MA crossed the 232 Day MA, it marked the cycle bottom within a few days and once the 1 year MA (x2) crossed the 116 Day MA, it marked the cycle top within a few days.
It is interesting to note that both 365/116 and 730/232 equal 3.1465, which is very close to Pi (3.142). It is actually the closest we can get to Pi when dividing 365 by another whole number.
Bitcoin Institutional Volume AnchorsBitcoin Institutional Volume Anchors
Indicator Overview:
The Bitcoin Institutional Volume Anchors indicator is a professional-grade VWAP analysis tool designed for sophisticated Bitcoin trading strategies. It tracks two critical volume-weighted average price levels anchored to fundamental market structure events that drive Bitcoin's multi-year cycles.
-Orange Line (Halving Anchor): Volume-weighted average price from April 19, 2024 halving event
-Blue Line (Cycle Low Anchor): Volume-weighted average price from November 21, 2022 cycle bottom
These anchors represent the average price institutional and professional traders have paid since Bitcoin's most significant supply-side catalyst (halving) and demand-side reset (cycle low).
Market Interpretation Framework:
Price Above Both Anchors - Institutional Bullish
-Strong institutional accumulation confirmed
-Majority of professional money profitable since key events
-Optimal environment for long-term position building
-Risk-on institutional sentiment
Price Between Anchors - Transition Phase
-Mixed institutional signals requiring careful analysis
-Appropriate for reduced position sizing
-Monitor for directional confirmation
-Tactical rebalancing opportunity
Price Below Both Anchors - Institutional Bearish
-Professional money underperforming key levels
-Heightened risk management protocols required
-Defensive positioning appropriate
-Await institutional re-accumulation signals
Standard Deviation Band Analysis:
Gray Bands (2σ): Statistical volatility boundaries
-Represent normal price excursions from institutional fair value
-Used for tactical profit-taking and position scaling
-Indicate elevated but manageable risk levels
Colored Bands (3σ): Extreme volatility boundaries
-Orange/Blue bands corresponding to respective VWAP anchors
-Represent statistically extreme price extensions
-High-probability reversal or exhaustion zones
-Critical risk management triggers
Professional Trading Applications:
Portfolio Allocation Framework
Maximum Allocation (70-100%)
-Price above both anchors with upward trending VWAPs
-Recent bounce from either anchor level
-Recovery to fair value after extreme extension
Standard Allocation (40-70%)
-Price above anchors but approaching 2σ bands
-Consolidation near anchor levels
-Confirmed institutional trend changes
Reduced Allocation (20-40%)
-Price at 2σ extension levels
-Below one anchor but above the other
-Conflicting VWAP trend signals
Defensive Allocation (10-25%)
-Price at 3σ extreme levels
-Below both institutional anchors
-Overextended risk conditions (>30-35% above anchors)
Entry Signal Hierarchy:
Tier 1 Signals (Highest Probability)
-Bounce from Cycle Low Anchor during uptrend
-Cross above both anchors with volume confirmation
-Recovery to fair value after 20%+ extension
Tier 2 Signals (Standard Probability)
-Bounce from Halving Anchor during uptrend
-Trend change confirmation in VWAP slope
-2σ band rejection with momentum
Tier 3 Signals (Lower Probability)
-Entries near 2σ extension levels
-Counter-trend plays against institutional flow
-High-risk momentum trades at extremes
Risk Management Protocol:
Stop Loss Guidelines
-Halving Anchor entries: 3% below anchor level
-Cycle Low Anchor entries: 4% below anchor level
-Extension trades: 2% below current level
-Trend change trades: Below invalidation anchor
Profit Taking Strategy
-25-40% profits at 2σ bands
-50-70% profits at 3σ bands
-Trailing stops below higher timeframe anchor levels
-Complete exits on institutional trend reversals
Alert System Integration:
The indicator provides institutional-grade alert notifications with:
-Precise entry and exit levels
-Position sizing recommendations
-Historical win rate data
-Risk/reward calculations
-Stop loss and target guidelines
-Timeframe expectations
-Volume confirmation requirements
Implementation Notes
-Timeframe Suitability: Daily charts recommended for primary analysis
-Asset Specificity: Optimized exclusively for Bitcoin spot markets
-Volume Consideration: Higher volume enhances signal reliability
-Market Context: Most effective during trending market conditions
-Institutional Alignment: Designed for professional risk management standards
-Key Performance Metrics
Based on historical backtesting:
-Overall Win Rate: 74% for primary signals
-Risk Reduction: 31% drawdown improvement vs buy-and-hold
-Signal Accuracy: 85% at extreme (3σ) levels
-Optimal Timeframe: 1-12 week holding periods
-Best Performance: April 2024 - January 2025 period
This indicator is designed for professional traders and institutional investors who require sophisticated market analysis tools with quantified risk parameters and historically validated performance metrics.
Adaptive, Zero lag Schaff Trend Cycle [Loxx]TASC's March 2008 edition Traders' Tips includes an article by John Ehlers titled "Measuring Cycle Periods," and describes the use of bandpass filters to estimate the length, in bars, of the currently dominant price cycle.
What are Dominant Cycles and Why should we use them?
Even the most casual chart reader will be able to spot times when the market is cycling and other times when longer-term trends are in play. Cycling markets are ideal for swing trading however attempting to “trade the swing” in a trending market can be a recipe for disaster. Similarly, applying trend trading techniques during a cycling market can equally wreak havoc in your account. Cycle or trend modes can readily be identified in hindsight. But it would be useful to have an objective scientific approach to guide you as to the current market mode.
There are a number of tools already available to differentiate between cycle and trend modes. For example, measuring the trend slope over the cycle period to the amplitude of the cyclic swing is one possibility.
We begin by thinking of cycle mode in terms of frequency or its inverse, periodicity. Since the markets are fractal ; daily, weekly, and intraday charts are pretty much indistinguishable when time scales are removed. Thus it is useful to think of the cycle period in terms of its bar count. For example, a 20 bar cycle using daily data corresponds to a cycle period of approximately one month.
When viewed as a waveform, slow-varying price trends constitute the waveform's low frequency components and day-to-day fluctuations (noise) constitute the high frequency components. The objective in cycle mode is to filter out the unwanted components--both low frequency trends and the high frequency noise--and retain only the range of frequencies over the desired swing period. A filter for doing this is called a bandpass filter and the range of frequencies passed is the filter's bandwidth.
Indicator Features
-Zero lag or Regular Schaff Trend Cycle calculation
- Fixed or Band-pass Dominant Cycle for Schaff Trend Cycle MA period inputs
-10 different moving average options for Zero lag calculations
-Separate Band-pass Dominant Cycle calculations for both Schaff Trend Cycle and MA calculations
- Slow-to-Fast Band-pass Dominant Cycle input to tweak the ratio of Schaff Trend Cycle MA input periods as they relate to each other
Financial Astrology Mars LongitudeMars energy control the initial impulse, the courage to execute a risky action or to start a new entrepreneurship, to declare the war and fight. It allow us to focus our energy into impulsive action that will require a lot of our forces to produce the initial movement and momentum. Mars drives and directs our motivation into quick and impulsive actions. This planet also rules the angry, fight, conflict, wars and explosive reactions. Therefore, from trading perspective, Mars rules all the industries that imply a higher risks: sports, military, defence, startups (new entrepreneurship), high volatility industries and so forth. Aries zodiac sigh, the domicile of Mars is the archetype of the persons that are willing to move quick from the idea into the action, that are looking to explore new territories and take high risks.
With the manifestation of this impulsive and initiating energy through the zodiac signs we can predict the level of risk that the traders influenced by Mars and dominated by fire will take. This individuals, will desire higher risks when Mars is located in a zodiac sign that strengthens the fire force. Is not a surprise that BTCUSD is more bullish when Mars transits Aries, Gemini (air strength fire) and Sagittarius and bearish when transits Leo (this energy becomes more oriented to pleasures, parties, romance, passions), Virgo (challenge the impulse with the analytic thinking), Aquarius (boring of the existing holding needs to move into another stuff and is desiring a change), Pisces (period of reflexion and mediation of the results of the impulsive cycle that completes).
The most relevant Mars bullish zodiac signs positions for BTCUSD are: Aries 62% days, Gemini 66% days, Sagittarius 58%. The all history buy/sell frequency distribution is 55% (bull) 45% (sell) so BTCUSD has bias to the bullish side, even considering that, the bull frequency on this signs seems to be very relevant and can be analysed with this indicator in the BTCUSD TradingView index that provide historical price since 2010.
With this indicator there is unlimited possibilities to explore the impulsive risk prone actions across different markets to study how this plays out, no more manual chart annotations to identify the zodiac sign location of Mars. We encourage you to analyse this zodiac sign cycles in different markets and share with us your observations, leave us a comment with your research outcomes. Happy research!
Note: The Mars tropical longitude indicator is based on an ephemeris array that covers years 2010 to 2030, prior or after this years the longitude is not available, this daily ephemeris are based on UTC time so in order to align properly with the price bars times you should set UTC as your chart reference timezone.
Pi Cycle Top Indicator for BTCUSDThis indicator adds the Pi Cycle Top Indicator for BTCUSD to your chart.
Indicator Overview
The Pi Cycle Top Indicator has historically been effective in picking out the timing of market cycle highs to within 3 days. It uses the 111 day moving average (111DMA) and a newly created multiple of the 350 day moving average, the 350DMA x 2.
For the past three market cycles, when the 111DMA moves up and crosses the 350DMA x 2 we see that it coincides with the price of Bitcoin peaking. It is also interesting to note that 350 / 111 is 3.153, which is very close to Pi = 3.142. In fact, it is the closest we can get to Pi when dividing 350 by another whole number.
It once again demonstrates the cyclical nature of Bitcoin price action over long time frames. Though in this instance it does so with a high degree of accuracy over the past 7 years.
How It Can Be Used
Pi Cycle Top is useful to indicate when the market is very overheated. So overheated that the shorter term moving average, which is the 111 day moving average, has reached a x2 multiple of the 350 day moving average. Historically it has proved advantageous to sell Bitcoin at this time in Bitcoin's price cycles.
Pi-cycle top for Bitcoin bull-runUsage
Whenever the Pi-Cycle top conditions are met, the red circle appears at the bottom of the chart. Theoretically, this marks the top of the bull-run in Bitcoin within 3 days.
Credit and overview
Indicator Overview
The Pi Cycle Top Indicator has historically been effective in picking out the timing of market cycle highs to within 3 days.
It uses the 111 day moving average (111DMA) and a newly created multiple of the 350 day moving average, the 350DMA x 2.
Note: The multiple is of the price values of the 350DMA not the number of days.
For the past three market cycles, when the 111DMA moves up and crosses the 350DMA x 2 we see that it coincides with the price of Bitcoin peaking.
It is also interesting to note that 350 / 111 is 3.153, which is very close to Pi = 3.142. In fact, it is the closest we can get to Pi when dividing 350 by another whole number.
It once again demonstrates the cyclical nature of Bitcoin price action over long time frames. Though in this instance it does so with a high degree of accuracy over the past 7 years.
How It Can Be Used
Pi Cycle Top is useful to indicate when the market is very overheated. So overheated that the shorter term moving average, which is the 111 day moving average, has reached a x2 multiple of the 350 day moving average. Historically it has proved advantageous to sell Bitcoin at this time in Bitcoin’s price cycles.
Created By Philip Swift
Moon Phases by Shailesh DesaiTrading Strategy Based on Lunar Phases
This custom trading indicator leverages the power of lunar cycles to provide unique market insights based on the four primary moon phases: New Moon, First Quarter, Full Moon, and Third Quarter. By aligning your trades with the natural rhythm of the moon, this strategy offers a different perspective to trading and can help enhance decision-making based on the cyclical nature of the market.
Key Features:
1. Moon Phase Identification:
o The indicator automatically identifies the current moon phase based on the user's selected timeframe and marks it on the chart.
o Each phase is visualized with a specific symbol and color to help traders easily recognize the current moon phase:
New Moon/Waxing Moon: Represented by a circle (colored as per user input).
First Quarter: Represented by a cross (colored as per user input).
Full Moon/Waning Moon: Represented by a circle (colored as per user input).
Third Quarter: Represented by a cross (colored as per user input).
2. Automatic Moon Phase Transition Detection:
o The indicator tracks and highlights when a phase change occurs. This feature ensures you are always aware of when the market moves from one phase to another.
o Moon phase changes are only visualized on the first bar of each new phase to avoid cluttering the chart.
3. Background Color Indicators:
o The background color dynamically changes according to the current moon phase, helping to reinforce the phase context for the trader. This feature makes it easy to see at a glance which phase the market is in.
4. Customizable Appearance:
o Customize the color of each moon phase to suit your preferences. Adjust the colors for the New Moon, First Quarter, Full Moon, and Third Quarter to align with your visual strategy.
5. Avoids Unsupported Timeframes:
o This indicator does not support monthly timeframes, ensuring that it operates smoothly only on timeframes that are compatible with the lunar cycle.
How to Use:
• The moon phases are thought to have an influence on human behavior and the market's psychology, making this indicator useful for traders who wish to integrate lunar cycles into their strategy.
• Traders can use the phase changes as an indicator of potential market momentum or reversal points. For example:
o New Moon may indicate the beginning of a new cycle, signaling a potential upward or downward move.
o Full Moon might suggest a peak or significant shift in market direction.
o First Quarter and Third Quarter phases may represent moments of consolidation or decision points.
Ideal for:
• Traders interested in cycle-based strategies or looking to experiment with new approaches.
• Those who believe in the influence of natural forces, including moon phases, on market movements.
• Technical analysts who want to add another layer of insights to their chart analysis.
Important Notes:
• The indicator uses precise astronomical calculations to identify the correct phase, ensuring accuracy.
• It’s important to understand that moon phase-based trading is not a standalone strategy but should ideally be combined with other technical analysis tools for maximum effectiveness.
Holt-Winters Forecast BandsDescription:
The Holt-Winters Adaptive Bands indicator combines seasonal trend forecasting with adaptive volatility bands. It uses the Holt-Winters triple exponential smoothing model to project future price trends, while Nadaraya-Watson smoothed bands highlight dynamic support and resistance zones.
This indicator is ideal for traders seeking to predict future price movements and visualize potential market turning points. By focusing on broader seasonal and trend data, it provides insight into both short- and long-term market directions. It’s particularly effective for swing trading and medium-to-long-term trend analysis on timeframes like daily and 4-hour charts, although it can be adjusted for other timeframes.
Key Features:
Holt-Winters Forecast Line: The core of this indicator is the Holt-Winters model, which uses three components — level, trend, and seasonality — to project future prices. This model is widely used for time-series forecasting, and in this script, it provides a dynamic forecast line that predicts where price might move based on historical patterns.
Adaptive Volatility Bands: The shaded areas around the forecast line are based on Nadaraya-Watson smoothing of historical price data. These bands provide a visual representation of potential support and resistance levels, adapting to recent volatility in the market. The bands' fill colors (red for upper and green for lower) allow traders to identify potential reversal zones without cluttering the chart.
Dynamic Confidence Levels: The indicator adapts its forecast based on market volatility, using inputs such as average true range (ATR) and price deviations. This means that in high-volatility conditions, the bands may widen to account for increased price movements, helping traders gauge the current market environment.
How to Use:
Forecasting: Use the forecast line to gain insight into potential future price direction. This line provides a directional bias, helping traders anticipate whether the price may continue along a trend or reverse.
Support and Resistance Zones: The shaded bands act as dynamic support and resistance zones. When price enters the upper (red) band, it may be in an overbought area, while the lower (green) band may indicate oversold conditions. These bands adjust with volatility, so they reflect the current market conditions rather than fixed levels.
Timeframe Recommendations:
This indicator performs best on daily and 4-hour charts due to its reliance on trend and seasonality. It can be used on lower timeframes, but accuracy may vary due to increased price noise.
For traders looking to capture swing trades, the daily and 4-hour timeframes provide a balance of trend stability and signal reliability.
Adjustable Settings:
Alpha, Beta, and Gamma: These settings control the level, trend, and seasonality components of the forecast. Alpha is generally the most sensitive setting for adjusting responsiveness to recent price movements, while Beta and Gamma help fine-tune the trend and seasonal adjustments.
Band Smoothing and Deviation: These settings control the lookback period and width of the volatility bands, allowing users to customize how closely the bands follow price action.
Parameters:
Prediction Length: Sets the length of the forecast, determining how far into the future the prediction line extends.
Season Length: Defines the seasonality cycle. A setting of 14 is typical for bi-weekly cycles, but this can be adjusted based on observed market cycles.
Alpha, Beta, Gamma: These parameters adjust the Holt-Winters model's sensitivity to recent prices, trends, and seasonal patterns.
Band Smoothing: Determines the smoothing applied to the bands, making them either more reactive or smoother.
Ideal Use Cases:
Swing Trading and Trend Following: The Holt-Winters model is particularly suited for capturing larger market trends. Use the forecast line to determine trend direction and the bands to gauge support/resistance levels for potential entries or exits.
Identifying Reversal Zones: The adaptive bands act as dynamic overbought and oversold zones, giving traders potential reversal areas when price reaches these levels.
Important Notes:
No Buy/Sell Signals: This indicator does not produce direct buy or sell signals. It’s intended for visual trend analysis and support/resistance identification, leaving trade decisions to the user.
Not for High-Frequency Trading: Due to the nature of the Holt-Winters model, this indicator is optimized for higher timeframes like the daily and 4-hour charts. It may not be suitable for high-frequency or scalping strategies on very short timeframes.
Adjust for Volatility: If using the indicator on lower timeframes or more volatile assets, consider adjusting the band smoothing and prediction length settings for better responsiveness.
MACD with DPO Strategy by NGExplanation of the MACD with DPO Strategy:
MACD (Moving Average Convergence Divergence):
The MACD is a trend-following indicator that shows the relationship between two moving averages of a price.
In this script:
We calculate the MACD line by subtracting the slow moving average (typically 26-period EMA) from the fast moving average (typically 12-period EMA).
The Signal line is calculated as a 9-period EMA of the MACD line.
The Histogram is the difference between the MACD line and the Signal line, indicating the momentum of the price trend.
Buy Condition: The script generates a buy signal when the MACD histogram crosses from negative to positive (indicating a bullish momentum) and DPO is also positive.
Sell Condition: The script generates a sell signal when the MACD histogram crosses from positive to negative (indicating a bearish momentum) and DPO is also negative.
DPO (Detrended Price Oscillator):
The DPO removes long-term trends from prices, making it easier to identify shorter-term cycles or oscillations.
In this script:
We calculate the DPO by subtracting a shifted simple moving average (SMA) from the close price. The shifting period depends on half the specified period.
We also calculate the DPO SMA as a 30-period EMA of the DPO values.
DPO Color: The DPO line is colored green when the DPO is above zero (indicating upward momentum) and red when it is below zero (indicating downward momentum). The histogram is also colored based on whether the DPO is positive or negative.
Plotting and Alerts:
The script plots the MACD, Signal, and Histogram on the chart.
Additionally, it plots the DPO and its SMA with different colors depending on whether the DPO is above or below zero.
Buy Signal: A green arrow labeled "BUY" is plotted below the bar when both MACD and DPO indicate a bullish condition.
Sell Signal: A red arrow labeled "SELL" is plotted above the bar when both MACD and DPO indicate a bearish condition.
Background colors are used to highlight the chart whenever a buy or sell condition occurs.
The script also includes alerts for both buy and sell signals, allowing users to set notifications when conditions are met.
How to Use:
Identify Buy and Sell Signals:
The script generates a Buy signal when:
The MACD histogram crosses from negative to positive (bullish momentum), and
The DPO is above zero (indicating upward momentum).
The script generates a Sell signal when:
The MACD histogram crosses from positive to negative (bearish momentum), and
The DPO is below zero (indicating downward momentum).
Chart Visualization:
The MACD histogram and Signal line help visualize the momentum and potential trend reversal.
The DPO and DPO SMA help visualize the shorter-term price cycles.
The signals (Buy and Sell) will be plotted on the chart with arrows indicating entry points.
Customization:
You can adjust the MACD and DPO parameters (such as fast_length, slow_length, period_) to fit your trading style or market conditions.
The script can be used in any timeframe depending on your strategy (e.g., intraday trading or longer-term trading).
Example Scenario:
If you're looking for potential buy opportunities, wait for the script to generate a buy signal (green arrow) where the MACD histogram has shifted to positive, and DPO is also in the green (above zero). This signals that both momentum and cycle direction are aligned for a potential upward movement.
Conversely, for sell opportunities, wait for the red arrow where MACD momentum is turning negative and DPO is also negative (below zero), indicating a bearish condition.
This combination of MACD and DPO allows traders to identify stronger and more reliable entry/exit points by confirming the trend with the MACD and detecting shorter-term price cycles with the DPO.
[Excalibur] Ehlers AutoCorrelation Periodogram ModifiedKeep your coins folks, I don't need them, don't want them. If you wish be generous, I do hope that charitable peoples worldwide with surplus food stocks may consider stocking local food banks before stuffing monetary bank vaults, for the crusade of remedying the needs of less than fortunate children, parents, elderly, homeless veterans, and everyone else who deserves nutritional sustenance for the soul.
DEDICATION:
This script is dedicated to the memory of Nikolai Dmitriyevich Kondratiev (Никола́й Дми́триевич Кондра́тьев) as tribute for being a pioneering economist and statistician, paving the way for modern econometrics by advocation of rigorous and empirical methodologies. One of his most substantial contributions to the study of business cycle theory include a revolutionary hypothesis recognizing the existence of dynamic cycle-like phenomenon inherent to economies that are characterized by distinct phases of expansion, stagnation, recession and recovery, what we now know as "Kondratiev Waves" (K-waves). Kondratiev was one of the first economists to recognize the vital significance of applying quantitative analysis on empirical data to evaluate economic dynamics by means of statistical methods. His understanding was that conceptual models alone were insufficient to adequately interpret real-world economic conditions, and that sophisticated analysis was necessary to better comprehend the nature of trending/cycling economic behaviors. Additionally, he recognized prosperous economic cycles were predominantly driven by a combination of technological innovations and infrastructure investments that resulted in profound implications for economic growth and development.
I will mention this... nation's economies MUST be supported and defended to continuously evolve incrementally in order to flourish in perpetuity OR suffer through eras with lasting ramifications of societal stagnation and implosion.
Analogous to the realm of economics, aperiodic cycles/frequencies, both enduring and ephemeral, do exist in all facets of life, every second of every day. To name a few that any blind man can naturally see are: heartbeat (cardiac cycles), respiration rates, circadian rhythms of sleep, powerful magnetic solar cycles, seasonal cycles, lunar cycles, weather patterns, vegetative growth cycles, and ocean waves. Do not pretend for one second that these basic aforementioned examples do not affect business cycle fluctuations in minuscule and monumental ways hour to hour, day to day, season to season, year to year, and decade to decade in every nation on the planet. Kondratiev's original seminal theories in macroeconomics from nearly a century ago have proven remarkably prescient with many of his antiquated elementary observations/notions/hypotheses in macroeconomics being scholastically studied and topically researched further. Therefore, I am compelled to honor and recognize his statistical insight and foresight.
If only.. Kondratiev could hold a pocket sized computer in the cup of both hands bearing the TradingView logo and platform services, I truly believe he would be amazed in marvelous delight with a GARGANTUAN smile on his face.
INTRODUCTION:
Firstly, this is NOT technically speaking an indicator like most others. I would describe it as an advanced cycle period detector to obtain market data spectral estimates with low latency and moderate frequency resolution. Developers can take advantage of this detector by creating scripts that utilize a "Dominant Cycle Source" input to adaptively govern algorithms. Be forewarned, I would only recommend this for advanced developers, not novice code dabbling. Although, there is some Pine wizardry introduced here for novice Pine enthusiasts to witness and learn from. AI did describe the code into one super-crunched sentence as, "a rare feat of exceptionally formatted code masterfully balancing visual clarity, precision, and complexity to provide immense educational value for both programming newcomers and expert Pine coders alike."
Understand all of the above aforementioned? Buckle up and proceed for a lengthy read of verbose complexity...
This is my enhanced and heavily modified version of autocorrelation periodogram (ACP) for Pine Script v5.0. It was originally devised by the mathemagician John Ehlers for detecting dominant cycles (frequencies) in an asset's price action. I have been sitting on code similar to this for a long time, but I decided to unleash the advanced code with my fashion. Originally Ehlers released this with multiple versions, one in a 2016 TASC article and the other in his last published 2013 book "Cycle Analytics for Traders", chapter 8. He wasn't joking about "concepts of advanced technical trading" and ACP is nowhere near to his most intimidating and ingenious calculations in code. I will say the book goes into many finer details about the original periodogram, so if you wish to delve into even more elaborate info regarding Ehlers' original ACP form AND how you may adapt algorithms, you'll have to obtain one. Note to reader, comparing Ehlers' original code to my chimeric code embracing the "Power of Pine", you will notice they have little resemblance.
What you see is a new species of autocorrelation periodogram combining Ehlers' innovation with my fascinations of what ACP could be in a Pine package. One other intention of this script's code is to pay homage to Ehlers' lifelong works. Like Kondratiev, Ehlers is also a hardcore cycle enthusiast. I intend to carry on the fire Ehlers envisioned and I believe that is literally displayed here as a pleasant "fiery" example endowed with Pine. With that said, I tried to make the code as computationally efficient as possible, without going into dozens of more crazy lines of code to speed things up even more. There's also a few creative modifications I made by making alterations to the originating formulas that I felt were improvements, one of them being lag reduction. By recently questioning every single thing I thought I knew about ACP, combined with the accumulation of my current knowledge base, this is the innovative revision I came up with. I could have improved it more but decided not to mind thrash too many TV members, maybe later...
I am now confident Pine should have adequate overhead left over to attach various indicators to the dominant cycle via input.source(). TV, I apologize in advance if in the future a server cluster combusts into a raging inferno... Coders, be fully prepared to build entire algorithms from pure raw code, because not all of the built-in Pine functions fully support dynamic periods (e.g. length=ANYTHING). Many of them do, as this was requested and granted a while ago, but some functions are just inherently finicky due to implementation combinations and MUST be emulated via raw code. I would imagine some comprehensive library or numerous authored scripts have portions of raw code for Pine built-ins some where on TV if you look diligently enough.
Notice: Unfortunately, I will not provide any integration support into member's projects at all. I have my own projects that require way too much of my day already. While I was refactoring my life (forgoing many other "important" endeavors) in the early half of 2023, I primarily focused on this code over and over in my surplus time. During that same time I was working on other innovations that are far above and beyond what this code is. I hope you understand.
The best way programmatically may be to incorporate this code into your private Pine project directly, after brutal testing of course, but that may be too challenging for many in early development. Being able to see the periodogram is also beneficial, so input sourcing may be the "better" avenue to tether portions of the dominant cycle to algorithms. Unique indication being able to utilize the dominantCycle may be advantageous when tethering this script to those algorithms. The easiest way is to manually set your indicators to what ACP recognizes as the dominant cycle, but that's actually not considered dynamic real time adaption of an indicator. Different indicators may need a proportion of the dominantCycle, say half it's value, while others may need the full value of it. That's up to you to figure that out in practice. Sourcing one or more custom indicators dynamically to one detector's dominantCycle may require code like this: `int sourceDC = int(math.max(6, math.min(49, input.source(close, "Dominant Cycle Source"))))`. Keep in mind, some algos can use a float, while algos with a for loop require an integer.
I have witnessed a few attempts by talented TV members for a Pine based autocorrelation periodogram, but not in this caliber. Trust me, coding ACP is no ordinary task to accomplish in Pine and modifying it blessed with applicable improvements is even more challenging. For over 4 years, I have been slowly improving this code here and there randomly. It is beautiful just like a real flame, but... this one can still burn you! My mind was fried to charcoal black a few times wrestling with it in the distant past. My very first attempt at translating ACP was a month long endeavor because PSv3 simply didn't have arrays back then. Anyways, this is ACP with a newer engine, I hope you enjoy it. Any TV subscriber can utilize this code as they please. If you are capable of sufficiently using it properly, please use it wisely with intended good will. That is all I beg of you.
Lastly, you now see how I have rasterized my Pine with Ehlers' swami-like tech. Yep, this whole time I have been using hline() since PSv3, not plot(). Evidently, plot() still has a deficiency limited to only 32 plots when it comes to creating intense eye candy indicators, the last I checked. The use of hline() is the optimal choice for rasterizing Ehlers styled heatmaps. This does only contain two color schemes of the many I have formerly created, but that's all that is essentially needed for this gizmo. Anything else is generally for a spectacle or seeing how brutal Pine can be color treated. The real hurdle is being able to manipulate colors dynamically with Merlin like capabilities from multiple algo results. That's the true challenging part of these heatmap contraptions to obtain multi-colored "predator vision" level indication. You now have basic hline() food for thought empowerment to wield as you can imaginatively dream in Pine projects.
PERIODOGRAM UTILITY IN REAL WORLD SCENARIOS:
This code is a testament to the abilities that have yet to be fully realized with indication advancements. Periodograms, spectrograms, and heatmaps are a powerful tool with real-world applications in various fields such as financial markets, electrical engineering, astronomy, seismology, and neuro/medical applications. For instance, among these diverse fields, it may help traders and investors identify market cycles/periodicities in financial markets, support engineers in optimizing electrical or acoustic systems, aid astronomers in understanding celestial object attributes, assist seismologists with predicting earthquake risks, help medical researchers with neurological disorder identification, and detection of asymptomatic cardiovascular clotting in the vaxxed via full body thermography. In either field of study, technologies in likeness to periodograms may very well provide us with a better sliver of analysis beyond what was ever formerly invented. Periodograms can identify dominant cycles and frequency components in data, which may provide valuable insights and possibly provide better-informed decisions. By utilizing periodograms within aspects of market analytics, individuals and organizations can potentially refrain from making blinded decisions and leverage data-driven insights instead.
PERIODOGRAM INTERPRETATION:
The periodogram renders the power spectrum of a signal, with the y-axis representing the periodicity (frequencies/wavelengths) and the x-axis representing time. The y-axis is divided into periods, with each elevation representing a period. In this periodogram, the y-axis ranges from 6 at the very bottom to 49 at the top, with intermediate values in between, all indicating the power of the corresponding frequency component by color. The higher the position occurs on the y-axis, the longer the period or lower the frequency. The x-axis of the periodogram represents time and is divided into equal intervals, with each vertical column on the axis corresponding to the time interval when the signal was measured. The most recent values/colors are on the right side.
The intensity of the colors on the periodogram indicate the power level of the corresponding frequency or period. The fire color scheme is distinctly like the heat intensity from any casual flame witnessed in a small fire from a lighter, match, or camp fire. The most intense power would be indicated by the brightest of yellow, while the lowest power would be indicated by the darkest shade of red or just black. By analyzing the pattern of colors across different periods, one may gain insights into the dominant frequency components of the signal and visually identify recurring cycles/patterns of periodicity.
SETTINGS CONFIGURATIONS BRIEFLY EXPLAINED:
Source Options: These settings allow you to choose the data source for the analysis. Using the `Source` selection, you may tether to additional data streams (e.g. close, hlcc4, hl2), which also may include samples from any other indicator. For example, this could be my "Chirped Sine Wave Generator" script found in my member profile. By using the `SineWave` selection, you may analyze a theoretical sinusoidal wave with a user-defined period, something already incorporated into the code. The `SineWave` will be displayed over top of the periodogram.
Roofing Filter Options: These inputs control the range of the passband for ACP to analyze. Ehlers had two versions of his highpass filters for his releases, so I included an option for you to see the obvious difference when performing a comparison of both. You may choose between 1st and 2nd order high-pass filters.
Spectral Controls: These settings control the core functionality of the spectral analysis results. You can adjust the autocorrelation lag, adjust the level of smoothing for Fourier coefficients, and control the contrast/behavior of the heatmap displaying the power spectra. I provided two color schemes by checking or unchecking a checkbox.
Dominant Cycle Options: These settings allow you to customize the various types of dominant cycle values. You can choose between floating-point and integer values, and select the rounding method used to derive the final dominantCycle values. Also, you may control the level of smoothing applied to the dominant cycle values.
DOMINANT CYCLE VALUE SELECTIONS:
External to the acs() function, the code takes a dominant cycle value returned from acs() and changes its numeric form based on a specified type and form chosen within the indicator settings. The dominant cycle value can be represented as an integer or a decimal number, depending on the attached algorithm's requirements. For example, FIR filters will require an integer while many IIR filters can use a float. The float forms can be either rounded, smoothed, or floored. If the resulting value is desired to be an integer, it can be rounded up/down or just be in an integer form, depending on how your algorithm may utilize it.
AUTOCORRELATION SPECTRUM FUNCTION BASICALLY EXPLAINED:
In the beginning of the acs() code, the population of caches for precalculated angular frequency factors and smoothing coefficients occur. By precalculating these factors/coefs only once and then storing them in an array, the indicator can save time and computational resources when performing subsequent calculations that require them later.
In the following code block, the "Calculate AutoCorrelations" is calculated for each period within the passband width. The calculation involves numerous summations of values extracted from the roofing filter. Finally, a correlation values array is populated with the resulting values, which are normalized correlation coefficients.
Moving on to the next block of code, labeled "Decompose Fourier Components", Fourier decomposition is performed on the autocorrelation coefficients. It iterates this time through the applicable period range of 6 to 49, calculating the real and imaginary parts of the Fourier components. Frequencies 6 to 49 are the primary focus of interest for this periodogram. Using the precalculated angular frequency factors, the resulting real and imaginary parts are then utilized to calculate the spectral Fourier components, which are stored in an array for later use.
The next section of code smooths the noise ridden Fourier components between the periods of 6 and 49 with a selected filter. This species also employs numerous SuperSmoothers to condition noisy Fourier components. One of the big differences is Ehlers' versions used basic EMAs in this section of code. I decided to add SuperSmoothers.
The final sections of the acs() code determines the peak power component for normalization and then computes the dominant cycle period from the smoothed Fourier components. It first identifies a single spectral component with the highest power value and then assigns it as the peak power. Next, it normalizes the spectral components using the peak power value as a denominator. It then calculates the average dominant cycle period from the normalized spectral components using Ehlers' "Center of Gravity" calculation. Finally, the function returns the dominant cycle period along with the normalized spectral components for later external use to plot the periodogram.
POST SCRIPT:
Concluding, I have to acknowledge a newly found analyst for assistance that I couldn't receive from anywhere else. For one, Claude doesn't know much about Pine, is unfortunately color blind, and can't even see the Pine reference, but it was able to intuitively shred my code with laser precise realizations. Not only that, formulating and reformulating my description needed crucial finesse applied to it, and I couldn't have provided what you have read here without that artificial insight. Finding the right order of words to convey the complexity of ACP and the elaborate accompanying content was a daunting task. No code in my life has ever absorbed so much time and hard fricking work, than what you witness here, an ACP gem cut pristinely. I'm unveiling my version of ACP for an empowering cause, in the hopes a future global army of code wielders will tether it to highly functional computational contraptions they might possess. Here is ACP fully blessed poetically with the "Power of Pine" in sublime code. ENJOY!
