Z_Score.efs
EFSLibrary - Discussion Board
File Name: Z_Score.efs
Description:
Z-Score
Formula Parameters:
- Period : 20
Notes:
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.
Download File:
Z_Score.efs
EFS Code:
/********************************* Provided By: eSignal (Copyright c eSignal), a division of Interactive Data Corporation. 2009. All rights reserved. This sample eSignal Formula Script (EFS) is for educational purposes only and may be modified and saved under a new file name. eSignal is not responsible for the functionality once modified. eSignal reserves the right to modify and overwrite this EFS file with each new release. Description: Z-Score Version: 1.0 03/24/2009 Formula Parameters: Default: Period 20 Notes: 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. **********************************/ var fpArray = new Array(); var bInit = false; function preMain() { setStudyTitle("Z-Score"); setCursorLabelName("Z-Score", 0); setDefaultBarFgColor(Color.red, 0); addBand(0, PS_SOLID, 1, Color.lightgrey); var x=0; fpArray[x] = new FunctionParameter("Period", FunctionParameter.NUMBER); with(fpArray[x++]){ setLowerLimit(1); setDefault(20); } } var xZ_Score = null; function main(Period) { var nBarState = getBarState(); var nZ_Score = 0; if (nBarState == BARSTATE_ALLBARS) { if(Period == null) Period = 20; } if (bInit == false) { xZ_Score = efsInternal("Calc_Z_Score", Period, sma(Period), close()); bInit = true; } nZ_Score = xZ_Score.getValue(0); if (nZ_Score == null) return; return nZ_Score; } function Calc_Z_Score(Period, xMA, xClose) { var nRes = 0; var StdDev = 0; var SumSqr = 0; var counter = 0; if(xMA.getValue(0) == null) return; for(counter = 0; counter < Period; counter++) SumSqr += Math.pow((xClose.getValue(-counter) - xMA.getValue(0)), 2); StdDev = Math.sqrt(SumSqr / Period); nRes = (xClose.getValue(0) - xMA.getValue(0)) / StdDev; return nRes; }