Fast Z-ScoreIntroduction
The ability of the least squares moving average to provide a great low lag filter is something i always liked, however the least squares moving average can have other uses, one of them is using it with the z-score to provide a fast smoothing oscillator.
The Indicator
The indicator aim to provide fast and smooth results. length control the smoothness.
The calculation is inspired from my sample correlation coefficient estimation described here
Instead of using the difference between a moving average of period length/2 and a moving average of period length , we use the difference between a lsma of period length/2 and a lsma of period length , this difference is then divided by the standard deviation. All those calculations use the price smoothed by a moving average as source.
The yellow version don't divide the difference by a standard deviation, you can that it is less reactive. Both version have length = 200
Conclusion
I presented a smooth and responsive version of a z-score, the result could be used to estimate an even faster lsma by using the line rescaling technique and our indicator as correlation coefficient.
Hope you like it, feel free to modify it and share your results ! :)
Notes
I have been requested a lot of indicators lately, from mt4 translations to more complex time series analysis methods, this accumulation of work made that it is impossible for me to publish those within a short period of time, also some are really complex. I apologize in advance for the inconvenience, i will try to do my best !
Z-score
Trend Score by KIVANÇ fr3762Trend Score compares close prices between last close with previous closes by a certain period of time.
It's like momentum but gives a score +1 when close price is equal to or above (defaultly) 10 bars ago and gives a score of -1 when below.
calculation continues from default length to the 2 times of length.
Defaultly (for 10 bars length)
If Trend Score converges to 10; that means there's a strong uptrend
conversely if Trend Score converges to -10; that means a strong downtrend market is on.
Z-Score Strategy Backtest The author of this indicator is Veronique Valcu. The z-score (z) for a data
item x measures the distance (in standard deviations StdDev) and direction
of the item from its mean (U):
z = (x-StdDev) / U
A value of zero indicates that the data item x is equal to the mean U, while
positive or negative values show that the data item is above (x>U) or below
(x Values of +2 and -2 show that the data item is two standard deviations
above or below the chosen mean, respectively, and over 95.5% of all data
items are contained within these two horizontal references (see Figure 1).
We substitute x with the closing price C, the mean U with simple moving
average (SMA) of n periods (n), and StdDev with the standard deviation of
closing prices for n periods, the above formula becomes:
Z_score = (C - SMA(n)) / StdDev(C,n)
The z-score indicator is not new, but its use can be seen as a supplement to
Bollinger bands. It offers a simple way to assess the position of the price
vis-a-vis its resistance and support levels expressed by the Bollinger Bands.
In addition, crossings of z-score averages may signal the start or the end of
a tradable trend. Traders may take a step further and look for stronger signals
by identifying common crossing points of z-score, its average, and average of average.
You can change long to short in the Input Settings
Please, use it only for learning or paper trading. Do not for real trading.
MAC-Z Indicator [LazyBear]This indicator is a composite of MACD and Z-Score (requested by @ChartAt). The general idea is that counter-trend component of the Z-score is used to adjust/improve the trend component of the MACD. The advantage is that it is a more accurate and “assumption-free” and can more accurately describe how a market or stock actually works in a given time frame.
I have also added support to smooth out the MAC-Z using Laguerre filter (Thanks @TheLark for the excellent LMA). Note that smoothing removes the "noise" component additive of Z-Score, so you may miss some good signals. By default Laguerre smoothing is OFF, I suggest playing with the Gamma to see if you can find a proper trade-off value.
Theme credits --> @liw0
More info:
cssanalytics.wordpress.com
Z-Score The author of this indicator is Veronique Valcu. The z-score (z) for a data
item x measures the distance (in standard deviations StdDev) and direction
of the item from its mean (U):
z = (x-StdDev) / U
A value of zero indicates that the data item x is equal to the mean U, while
positive or negative values show that the data item is above (x>U) or below
(x Values of +2 and -2 show that the data item is two standard deviations
above or below the chosen mean, respectively, and over 95.5% of all data
items are contained within these two horizontal references (see Figure 1).
We substitute x with the closing price C, the mean U with simple moving
average (SMA) of n periods (n), and StdDev with the standard deviation of
closing prices for n periods, the above formula becomes:
Z_score = (C - SMA(n)) / StdDev(C,n)
The z-score indicator is not new, but its use can be seen as a supplement to
Bollinger bands. It offers a simple way to assess the position of the price
vis-a-vis its resistance and support levels expressed by the Bollinger Bands.
In addition, crossings of z-score averages may signal the start or the end of
a tradable trend. Traders may take a step further and look for stronger signals
by identifying common crossing points of z-score, its average, and average of average.
