Z-Score The z-score is a way of counting the number of standard deviations between a given data value and the mean of the data set.
Z-score = (x̄ - μ) / (σ / √ n)
x̄ = sample mean (using the array.avg function = array(a,close ), where i = 1 to 21)
μ = population mean ( = avg(close, n))
σ = standard deviation of the population ( = stdev(close,n))
n = number of 'close' or trading day closes
n = input
... Note: The previous indicator is part of a larger series of indicators
Arrays
Resampling Filter Pack [DW]This is an experimental study that calculates filter values at user defined sample rates.
This study is aimed to provide users with alternative functions for filtering price at custom sample rates.
First, source data is resampled using the desired rate and cycle offset. The highest possible rate is 1 bar per sample (BPS).
There are three resampling methods to choose from:
-> BPS - Resamples based on the number of bars.
-> Interval - Resamples based on time in multiples of current charting timeframe.
-> PA - Resamples based on changes in price action by a specified size. The PA algorithm in this script is derived from my Range Filter algorithm.
The range for PA method can be sized in points, pips, ticks, % of price, ATR, average change, and absolute quantity.
Then, the data is passed through one of my custom built filter functions designed to calculate filter values upon trigger conditions rather than bars.
In this study, these functions are used to calculate resampled prices based on bar rates, but they can be used and modified for a number of purposes.
The available conditional sampling filters in this study are:
-> Simple Moving Average (SMA)
-> Exponential Moving Average (EMA)
-> Zero Lag Exponential Moving Average (ZLEMA)
-> Double Exponential Moving Average (DEMA)
-> Rolling Moving Average (RMA)
-> Weighted Moving Average (WMA)
-> Hull Moving Average (HMA)
-> Exponentially Weighted Hull Moving Average (EWHMA)
-> Two Pole Butterworth Low Pass Filter (BLP)
-> Two Pole Gaussian Low Pass Filter (GLP)
-> Super Smoother Filter (SSF)
Downsampling is a powerful filtering approach that can be applied in numerous ways. However, it does suffer from a trade off, like most studies do.
Reducing the sample rate will completely eliminate certain levels of noise, at the cost of some spectral distortion. The lower your sample rate is, the more distortion you'll see.
With that being said, for analyzing trends, downsampling may prove to be one of your best friends!
Pinescript Bubble Sort using ArraysThe new feature of arrays allows for a multitude of new possibilities within Pinescript. This script implements a bubble sort function with most probable efficiency of О(n^2) with a best-case being O(n). This sort does not require large amounts of memory to process and has advantages when sorting small lists of data.
The main advantages: Bubble sort is an in-place sorting algorithm. It does not require extra memory or even stack space like in the case of merge sort or quicksort.
The main disadvantages: In the worst case the time complexity is equal to O(n^2) which is not efficient in comparison to other sorts which can have a time complexity of O(n*logn).
The Pseudocode for a bubble sort is as follows:
begin BubbleSort(list)
for all elements of list
if list > list
swap(list , list )
end if
end for
return list
end BubbleSort
The results of the sort are plotted against the unsorted list and overlayed on the chart.
A big thanks to Alex Grover for the help.
Range Filter [DW]This is an experimental study designed to filter out minor price action for a clearer view of trends.
Inspired by the QQE's volatility filter, this filter applies the process directly to price rather than to a smoothed RSI.
First, a smooth average price range is calculated for the basis of the filter and multiplied by a specified amount.
Next, the filter is calculated by gating price movements that do not exceed the specified range.
Lastly the target ranges are plotted to display the prices that will trigger filter movement.
Custom bar colors are included. The color scheme is based on the filtered price trend.
