March 2010

eSIGNAL: EMPIRICAL MODE DECOMPOSITION

For this month’s Traders’ Tip, we’ve provided the formulas BandpassFilter.efs, ExtractingTrend.efs, and EmpiricalMode­Decomposition.efs, based on the formula code provided in the article by John Ehlers and Ric Way in this issue, “Empirical Mode Decomposition.”

All studies contain the formula parameters length, delta, and price (price source), which may be configured through the Edit Studies window (Advanced Chart menu → Edit Studies). The empirical mode decomposition formula also contains a formula parameter for fraction.

BandpassFilter.efs

/*********************************
Provided By: 
   eSignal (Copyright c eSignal), a division of Interactive Data
   Corporation. 2010. 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:       
    Bandpass Filter
   
Version:            1.00  01/08/2010

Formula Parameters:                     Default:
    Length                              20
    Delta                               0.5
    Price                               hl2
   
Notes:
  The related article is copyrighted material. If you are not a 
  subscriber of Stocks & Commodities, please visit 
  www.traders.com.

**********************************/
var fpArray = new Array();
var bInit = false;
var bVersion = null;

function preMain() {
    setPriceStudy(false);
    setShowCursorLabel(true);
    setShowTitleParameters(false);
    setStudyTitle("Bandpass Filter");
    setCursorLabelName("Bandpass Filter", 0);
    setDefaultBarFgColor(Color.red, 0);
    setPlotType(PLOTTYPE_LINE, 0);
    setDefaultBarThickness(2, 0);
    var x=0;
    fpArray[x] = new FunctionParameter("Length", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Length");
        setLowerLimit(1);		
        setDefault(20);
    }   
    fpArray[x] = new FunctionParameter("Delta", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Delta");
        setLowerLimit(0.00001);		
        setDefault(0.5);
    }       
	fpArray[x] = new FunctionParameter("Price", FunctionParameter.STRING);
	with(fpArray[x++]){
        setName("Price Source");
        addOption("open");
        addOption("high");
        addOption("low");
        addOption("close");
        addOption("hl2");
        addOption("hlc3");
        addOption("ohlc4");
        setDefault("hl2");
    }   
}

var xBandpassFilter = null;

function main(Length, Delta, Price) {
var nBarState = getBarState();
var nBandpassFilter = 0;
    if (bVersion == null) bVersion = verify();
    if (bVersion == false) return;  
    if (nBarState == BARSTATE_ALLBARS) {
        if (Length == null) Length = 20;
        if (Delta == null) Delta = 0.5;
        if (Price == null) Price = "hl2";       
    }   
    if (!bInit) {
        addBand(0, PS_SOLID, 1, Color.blue, "Zero");   
        xBandpassFilter = efsInternal("Calc_BandpassFilter", Length, Delta, Price);
        bInit = true;
    }
    nBandpassFilter = xBandpassFilter.getValue(0);
    if (nBandpassFilter == null) return;
    return nBandpassFilter;
}

var bSecondInit = false;
var xPrice = null;

function Calc_BandpassFilter(Length, Delta, Price) {
var gamma = 0;
var alpha = 0;
var beta = 0;
var BP = 0;
var BP1 = ref(-1);
var BP2 = ref(-2);
    if (bSecondInit == false) {
        xPrice = eval(Price)();
        bSecondInit = true;
    }
    if (xPrice.getValue(-2) == null) return;
    beta = Math.cos(Math.PI * (360 / Length) / 180);
    gamma = 1 / Math.cos(Math.PI * (720 * Delta / Length) / 180);
    alpha = gamma - Math.sqrt(gamma * gamma - 1);
    BP = 0.5 * (1 - alpha) * (xPrice.getValue(0) - xPrice.getValue(-2)) + beta * (1 + alpha) * BP1 - alpha * BP2;
    return BP;
}

function verify() {
    var b = false;
    if (getBuildNumber() < 779) {
        drawTextAbsolute(5, 35, "This study requires version 8.0 or later.",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "error");
        drawTextAbsolute(5, 20, "Click HERE to upgrade.@URL=http://www.esignal.com/download/default.asp",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "upgrade");
        return b;
    } else {
        b = true;
    }
    return b;
}

ExtractingTrend.efs

/*********************************
Provided By: 
    eSignal (Copyright c eSignal), a division of Interactive Data
    Corporation. 2010. 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:       
    Extracting The Trend

Version:            1.00  01/08/2010

Formula Parameters:                     Default:
    Length                              20
    Delta                               0.5
    Price                               hl2

Notes:
   The related article is copyrighted material. If you are not a
   subscriber of Stocks & Commodities, please visit
   www.traders.com.

**********************************/
var fpArray = new Array();
var bInit = false;
var bVersion = null;

function preMain() {
    setPriceStudy(false);
    setShowCursorLabel(true);
    setShowTitleParameters(false);
    setStudyTitle("Extracting The Trend");
    setCursorLabelName("ExTrend", 0);
    setDefaultBarFgColor(Color.red, 0);
    setPlotType(PLOTTYPE_LINE, 0);
    setDefaultBarThickness(2, 0);
    var x=0;
    fpArray[x] = new FunctionParameter("Length", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Length");
        setLowerLimit(1);		
        setDefault(20);
    }   
    fpArray[x] = new FunctionParameter("Delta", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Delta");
        setLowerLimit(0.00001);		
        setDefault(0.5);
    }       
	fpArray[x] = new FunctionParameter("Price", FunctionParameter.STRING);
	with(fpArray[x++]){
        setName("Price Source");
        addOption("open");
        addOption("high");
        addOption("low");
        addOption("close");
        addOption("hl2");
        addOption("hlc3");
        addOption("ohlc4");
        setDefault("hl2");
    }   
}

var xBandpassFilter = null;
var xTrend = null;

function main(Length, Delta, Price) {
var nBarState = getBarState();
var nTrend = 0;
    if (bVersion == null) bVersion = verify();
    if (bVersion == false) return;  
    if (nBarState == BARSTATE_ALLBARS) {
        if (Length == null) Length = 20;
        if (Delta == null) Delta = 0.5;
        if (Price == null) Price = "hl2";       
    }   
    if (!bInit) {
        addBand(0, PS_SOLID, 1, Color.blue, "Zero");   
        xBandpassFilter = efsInternal("Calc_BandpassFilter", Length, Delta, Price);
        xTrend = sma(2 * Length, xBandpassFilter);
        bInit = true;
    }
    nTrend = xTrend.getValue(0);
    if (nTrend == null) return;
    return nTrend;
}

var bSecondInit = false;
var xPrice = null;

function Calc_BandpassFilter(Length, Delta, Price) {
var gamma = 0;
var alpha = 0;
var beta = 0;
var BP = 0;
var BP1 = ref(-1);
var BP2 = ref(-2);
    if (bSecondInit == false) {
        xPrice = eval(Price)();
        bSecondInit = true;
    }
    if (xPrice.getValue(-2) == null) return;
    beta = Math.cos(Math.PI * (360 / Length) / 180);
    gamma = 1 / Math.cos(Math.PI * (720 * Delta / Length) / 180);
    alpha = gamma - Math.sqrt(gamma * gamma - 1);
    BP = 0.5 * (1 - alpha) * (xPrice.getValue(0) - xPrice.getValue(-2)) + beta * (1 + alpha) * BP1 - alpha * BP2;
    return BP;
}

function verify() {
    var b = false;
    if (getBuildNumber() < 779) {
        drawTextAbsolute(5, 35, "This study requires version 8.0 or later.",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "error");
        drawTextAbsolute(5, 20, "Click HERE to upgrade.@URL=http://www.esignal.com/download/default.asp",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "upgrade");
        return b;
    } else {
        b = true;
    }
    return b;
}

EmpiricalModeDecomposition.efs

/*********************************
Provided By: 
   eSignal (Copyright c eSignal), a division of Interactive Data
   Corporation. 2010. 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:       
    Empirical Mode Decomposition

Version:            1.00  01/08/2010

Formula Parameters:                     Default:
    Length                              20
    Delta                               0.5
    Fraction                            0.1
    Price                               hl2

Notes:
   The related article is copyrighted material. If you are not a
   subscriber of Stocks & Commodities, please visit
   www.traders.com.

**********************************/
var fpArray = new Array();
var bInit = false;
var bVersion = null;

function preMain() {
    setPriceStudy(false);
    setShowCursorLabel(true);
    setShowTitleParameters(false);
    setStudyTitle("Empirical Mode Decomposition");
    setCursorLabelName("Mean", 0);
    setDefaultBarFgColor(Color.red, 0);
    setPlotType(PLOTTYPE_LINE, 0);
    setDefaultBarThickness(2, 0);
    setCursorLabelName("Peak", 1);
    setDefaultBarFgColor(Color.blue, 1);
    setPlotType(PLOTTYPE_LINE, 1);
    setDefaultBarThickness(2, 1);
    setCursorLabelName("Valley", 2);
    setDefaultBarFgColor(Color.blue, 2);
    setPlotType(PLOTTYPE_LINE, 2);
    setDefaultBarThickness(2, 2);
    var x=0;
    fpArray[x] = new FunctionParameter("Length", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Length");
        setLowerLimit(1);		
        setDefault(20);
    }   
    fpArray[x] = new FunctionParameter("Delta", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Delta");
        setLowerLimit(0.00001);		
        setDefault(0.5);
    }       
    fpArray[x] = new FunctionParameter("Fraction", FunctionParameter.NUMBER);
	with(fpArray[x++]){
        setName("Fraction");
        setLowerLimit(0.00001);		
        setDefault(0.1);
    }       
	fpArray[x] = new FunctionParameter("Price", FunctionParameter.STRING);
	with(fpArray[x++]){
        setName("Price Source");
        addOption("open");
        addOption("high");
        addOption("low");
        addOption("close");
        addOption("hl2");
        addOption("hlc3");
        addOption("ohlc4");
        setDefault("hl2");
    }   
}

var xEmpiricalModeDecomposition_Mean = null;
var xEmpiricalModeDecomposition_Peak = null;
var xEmpiricalModeDecomposition_Valley = null;

function main(Length, Delta, Fraction, Price) {
var nBarState = getBarState();
var nEmpiricalModeDecomposition_Mean = 0;
var nEmpiricalModeDecomposition_Peak = 0;
var nEmpiricalModeDecomposition_Valley = 0;
    if (bVersion == null) bVersion = verify();
    if (bVersion == false) return;  
    if (nBarState == BARSTATE_ALLBARS) {
        if (Length == null) Length = 20;
        if (Delta == null) Delta = 0.5;
        if (Fraction == null) Fraction = 0.1;       
        if (Price == null) Price = "hl2";       
    }   
    if (bInit == false) {
        xEmpiricalModeDecomposition_Mean = efsInternal("Calc_EmpiricalModeDecomposition", Length, Delta, Fraction, Price);
        xEmpiricalModeDecomposition_Peak = getSeries(xEmpiricalModeDecomposition_Mean, 1);
        xEmpiricalModeDecomposition_Valley = getSeries(xEmpiricalModeDecomposition_Mean, 2);
        bInit = true;
    }
    nEmpiricalModeDecomposition_Mean = xEmpiricalModeDecomposition_Mean.getValue(0);
    nEmpiricalModeDecomposition_Peak = xEmpiricalModeDecomposition_Peak.getValue(0);
    nEmpiricalModeDecomposition_Valley = xEmpiricalModeDecomposition_Valley.getValue(0);
    if (nEmpiricalModeDecomposition_Mean == null ||
        nEmpiricalModeDecomposition_Peak == null ||
        nEmpiricalModeDecomposition_Valley == null) return;
    return new Array(nEmpiricalModeDecomposition_Mean, nEmpiricalModeDecomposition_Peak, nEmpiricalModeDecomposition_Valley);
}

var bSecondInit = false;
var xMean = null;
var xAvrPeak = null;
var xAvrValley = null;

function Calc_EmpiricalModeDecomposition(Length, Delta, Fraction, Price) {
var nMean = 0;
var nAvrPeak = 0;
var nAvrValley = 0;
    if (bSecondInit == false) {
        xMean = efsInternal("Calc_Mean_Peak_Valley", Length, Delta, Price);
        xAvrPeak = sma(50, getSeries(xMean, 1));
        xAvrValley = sma(50, getSeries(xMean, 2));
        bSecondInit = true;
    }
    nMean = xMean.getValue(0);
    nAvrPeak = xAvrPeak.getValue(0);
    nAvrValley = xAvrValley.getValue(0);
    if (nMean == null || nAvrPeak == null || nAvrValley == null) return;
    nAvrPeak = Fraction * nAvrPeak;
    nAvrValley = Fraction * nAvrValley;
    return new Array(nMean, nAvrPeak, nAvrValley);
}

var bMPVInit = false;
var nPeak = 0;
var nValley = 0;

function Calc_Mean_Peak_Valley(Length, Delta, Price) {
var nMean = 0;
var BP = 0;
var BP1 = 0;
var BP2 = 0;
    if (bMPVInit == false) {
        xBandpassFilter = efsInternal("Calc_BandpassFilter", Length, Delta, Price);
        xMean = sma(2 * Length, xBandpassFilter);
        bMPVInit = true;
    }
    nMean = xMean.getValue(0);
    BP = xBandpassFilter.getValue(0);
    BP1 = xBandpassFilter.getValue(-1);
    BP2 = xBandpassFilter.getValue(-2);
    if (BP1 > BP && BP1 > BP2) {
        nPeak = BP1;
    }   
    if (BP1 < BP && BP1 < BP2) {
        nValley = BP1;   
    }   
    return new Array(nMean, nPeak, nValley);
}

var bThirdInit = false;
var xPrice = null;

function Calc_BandpassFilter(Length, Delta, Price) {
var gamma = 0;
var alpha = 0;
var beta = 0;
var BP = 0;
var BP1 = ref(-1);
var BP2 = ref(-2);
    if (bThirdInit == false) {
        xPrice = eval(Price)();
        bThirdInit = true;
    }
    if (xPrice.getValue(-2) == null) return;
    beta = Math.cos(Math.PI * (360 / Length) / 180);
    gamma = 1 / Math.cos(Math.PI * (720 * Delta / Length) / 180);
    alpha = gamma - Math.sqrt(gamma * gamma - 1);
    BP = 0.5 * (1 - alpha) * (xPrice.getValue(0) - xPrice.getValue(-2)) + beta * (1 + alpha) * BP1 - alpha * BP2;
    return BP;
}

function verify() {
    var b = false;
    if (getBuildNumber() < 779) {
        drawTextAbsolute(5, 35, "This study requires version 8.0 or later.",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "error");
        drawTextAbsolute(5, 20, "Click HERE to upgrade.@URL=http://www.esignal.com/download/default.asp",
            Color.white, Color.blue, Text.RELATIVETOBOTTOM|Text.RELATIVETOLEFT|Text.BOLD|Text.LEFT,
            null, 13, "upgrade");
        return b;
    } else {
        b = true;
    }
    return b;
}

To discuss this study or download complete copies of the formula code, please visit the Efs Library Discussion Board forum under the Forums link from the Support menu at www.esignal.com, or visit our Efs KnowledgeBase at http://www.esignal.com/support/kb/efs/. The eSignal formula scripts (Efs) are also available for copying and pasting from the Stocks & Commodities website at Traders.com.

A sample chart is shown in Figure 2.

Figure 2: eSIGNAL, Empirical Mode Decomposition

—Jason Keck
eSignal, a division of Interactive Data Corp.
800 815-8256, www.esignalcentral.com

BACK TO LIST

WEALTH-LAB: EMPIRICAL MODE DECOMPOSITION

For this month’s Traders’ Tip, we combined the ideas and indicators from “Empirical Mode Decomposition” by John Ehlers and Ric Way into a single script with a sample strategy in C# for Wealth-Lab 5.

While you can probably think of a dozen ways to use the cycle mode indicator and its thresholds, our sample strategy enters long trades when the cycle turns up within the threshold zone and exits on a closing profit of 4% or after five bars. The time-based exit was chosen purposely to be a quarter cycle in order to exit before the next downturn.

The strategy produced a slightly positive win rate and raw profit factor for the last six years of trading on the Dow Jones Industrial Average (Djia) and Nasdaq 100 index components (Figure 3)

Figure 3: WEALTH-LAB, Empirical Mode Decomposition. Here are some representative trades from our sample Wealth-Lab strategy based on John Ehlers and Ric Way’s empirical mode decomposition method.

WealthScript code (C#): 

using System;
using System.Collections.Generic;
using System.Text;
using System.Drawing;
using WealthLab;
using WealthLab.Indicators;

namespace WealthLab.Strategies
{
   public class EmpiricalModeDecomp : WealthScript
   {
      StrategyParameter _period;
      StrategyParameter _delta;
      StrategyParameter _fraction;
      
      public EmpiricalModeDecomp()
      {
         _period = CreateParameter("Period", 20, 5, 50, 1);
         _delta = CreateParameter("Delta", 0.5, 0.05, 1, 0.05);
         _fraction = CreateParameter("Fraction", 0.25, 0.1, 1, 0.05);
      }

      public DataSeries BandPassSeries(DataSeries ds, int period, double delta)
      {
         DataSeries res = new DataSeries(ds, "BandPassSeries(" + ds.Description + "," + period + "," + delta + ")");
         double beta = Math.Cos(2 * Math.PI / period);
         double gamma = 1/ Math.Cos(4 * Math.PI * delta / period);
         double alpha = gamma - Math.Sqrt(gamma * gamma - 1d);
         
         for (int bar = 2; bar < ds.Count; bar++)
         {
            res[bar] = 0.5 * (1 - alpha) * (ds[bar] - ds[bar - 2])
               + beta * (1 + alpha) * res[bar - 1] - alpha * res[bar - 2];
         }         
         return res; 
      }
      
      protected override void Execute()
      {            
         int per = _period.ValueInt;
         double delta = _delta.Value;
         double fraction = _fraction.Value;
         
         DataSeries bp = BandPassSeries(AveragePrice.Series(Bars), per, delta);
         DataSeries ema = EMA.Series(Close, 100, EMACalculation.Modern);
         DataSeries mean = SMA.Series(bp, 2 * per);
         mean.Description = "SMA(" + bp.Description + "," + 2 * per + ")";
         DataSeries peak = new DataSeries(Bars, "peak()");
         DataSeries valley = new DataSeries(Bars, "valley()");
         double pk = 0d; 
         double v = 0d;
         for(int bar = 2; bar < Bars.Count; bar++)
         {            
            if( bp[bar-1] > bp[bar] && bp[bar-1] > bp[bar-2] ) 
               pk = bp[bar - 1];
            if( bp[bar-1] < bp[bar] && bp[bar-1] < bp[bar-2] ) 
               v = bp[bar-1];
            peak[bar] = pk;
            valley[bar] = v;
         }         
         int avgPer = (int)(2.5 * per);
         DataSeries avgPeak = fraction * SMA.Series(peak, avgPer);
         DataSeries avgValley = fraction * SMA.Series(valley, avgPer);
         
         ChartPane cp = CreatePane( 40, true, false );
         DrawHorzLine(cp, 0d, Color.Black, LineStyle.Dashed, 1);
         PlotSeries(PricePane, ema, Color.Black, LineStyle.Solid, 1);
         PlotSeries(cp, avgPeak, Color.DodgerBlue, LineStyle.Solid, 1);
         PlotSeries(cp, avgValley, Color.DodgerBlue, LineStyle.Solid, 1);
         PlotSeries(cp, mean, Color.Orange, LineStyle.Solid, 2);
         
         /* Sample Trading Strategy */  
         for (int bar = 2 * 100; bar < Bars.Count; bar++)
         {
            bool setup = mean[bar] > avgValley[bar] 
               && mean[bar] < avgPeak[bar]
               && ema[bar] > ema[bar-1];
            
            if (IsLastPositionActive)
            {
               Position p = LastPosition;
               if (bar - p.EntryBar > 4)
                  SellAtMarket(bar + 1, p, "Time Based");
               else if (Close[bar] > p.EntryPrice * 1.04)
                  SellAtClose(bar, p, "Profit Target");
            }
            else if ( setup && TurnUp(bar, mean) )
            {               
               SetBackgroundColor(bar, Color.LightCyan);
               BuyAtMarket(bar + 1);   
            }
         }
      }
   }
}

—Robert Sucher
www.wealth-lab.com

BACK TO LIST

WORDEN BROTHERS STOCKFINDER: EMPIRICAL MODE DECOMPOSITION

The empirical mode decomposition setup described in “Empirical Mode Decomposition” by John Ehlers and Ric Way in this issue is easy to set up in StockFinder using RealCode.

You can add the indicator to your chart by clicking the “Add indicator/condition” button or by simply typing “/Empirical Mode” and choosing it from the list of available indicators.

Here is the code to display the empirical mode decomposition plot shown in Figure 5.

'# Cumulative
'# Period = UserInput.Integer = 20
'# Delta = UserInput.Single = 0.5
'# Fraction = UserInput.Single = 0.1
Static gamma As Single
Static alpha As Single
Static beta As Single
Static BP(2,2) As Single
Static Offset(2) As Integer
Static Trend As Single
Static Peak(1) As Single
Static Valley(1) As Single
Static AvgPeak As Single
Static AvgValley As Single
If isFirstBar Then
	beta = Math.Cos((360 / Period) * Math.PI / 180)
	gamma = 1 / Math.Cos((720 * delta / Period) * Math.PI / 180)
	alpha = gamma - ((gamma * gamma - 1) ^ .5)
	BP(2, 0) = 0
	BP(1, 0) = 0
	BP(0, 0) = 0
	BP(2, 1) = 0
	BP(1, 1) = 0
	BP(0, 1) = 0
	BP(2, 2) = 0
	BP(1, 2) = 0
	BP(0, 2) = 0
	Offset(0) = 2 * Period
	Offset(1) = Math.Max(Offset(0) + 1, 50)
	Offset(2) = Offset(0) + 2
	Trend = 0
	Peak(0) = 0
	Peak(1) = 0
	Valley(0) = 0
	Valley(1) = 0
	AvgPeak = 0
	AvgValley = 0
End If
If CurrentIndex >= 2 Then
	BP(2, 0) = BP(1, 0)
	BP(1, 0) = BP(0, 0)
	BP(0, 0) = .5 * (1 - alpha) * (Price.High + Price.Low _
		- Price.High(2) - Price.Low(2)) / 2 _
		+ beta * (1 + alpha) * BP(1, 0) - alpha * BP(2, 0)
	Trend += BP(0, 0) / Offset(0)
	If BP(1, 0) > BP(0, 0) AndAlso BP(1, 0) > BP(2, 0) Then Peak(0) = BP(1, 0)
	AvgPeak += Peak(0) / 50
	If BP(1, 0) < BP(0, 0) AndAlso BP(1, 0) < BP(2, 0) Then Valley(0) = BP(1, 0)
	AvgValley += Valley(0) / 50
	If CurrentIndex >= Offset(2) Then
		BP(2, 1) = BP(1, 1)
		BP(1, 1) = BP(0, 1)
		BP(0, 1) = .5 * (1 - alpha) * (Price.High(Offset(0)) + Price.Low(Offset(0)) _
			- Price.High(Offset(2)) - Price.Low(Offset(2))) / 2 _
			+ beta * (1 + alpha) * BP(1, 1) - alpha * BP(2, 1)
		Trend -= BP(0, 1) / Offset(0)
	End If
	If CurrentIndex >= 52 Then
		BP(2, 2) = BP(1, 2)
		BP(1, 2) = BP(0, 2)
		BP(0, 2) = .5 * (1 - alpha) * (Price.High(50) + Price.Low(50) _
			- Price.High(52) - Price.Low(52)) / 2 _
			+ beta * (1 + alpha) * BP(1, 2) - alpha * BP(2, 2)
		If BP(1, 2) > BP(0, 2) AndAlso BP(1, 2) > BP(2, 2) Then Peak(1) = BP(1, 2)
		AvgPeak -= Peak(0) / 50
		If BP(1, 2) < BP(0, 2) AndAlso BP(1, 2) < BP(2, 2) Then Valley(1) = BP(1, 2)
		AvgValley -= Valley(0) / 50
	End If
End If
If CurrentIndex >= Offset(1) Then
	OpenValue = Trend
	HighValue = Fraction * AvgPeak
	LowValue = Fraction * AvgValley
	Plot = Trend
Else
	OpenValue = Single.NaN
	HighValue = Single.NaN
	LowValue = Single.NaN
	Plot = Single.NaN
End If

Figure 5: STOCKFINDER, Empirical Mode Decomposition. The empirical mode decomposition line is plotted along with peak and valley lines to identify when a stock is cycling (cyan price bars), entering an uptrend (green arrows), or entering a downtrend (red arrows).

RealCode is based on the Microsoft Visual Basic.Net framework and uses the Visual Basic (VB) language syntax. RealCode is compiled into a .Net assembly and run by the StockFinder application. RealCode is fully compiled and runs at the same machine-language level as the application itself, with the flexibility of run-time development and assembly that you get by writing your own custom code.

To use the indicators, rules and charts in this Traders’ Tip, you will need the StockFinder software. For more information or to start a free trial, please visit www.StockFinder.com.

— Bruce Loebrich and Patrick Argo
Worden Brothers, Inc.
www.StockFinder.com

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AIQ: FLAT-BASE BREAKOUT SYSTEM

The Aiq code is provided here for the flat-base breakout system, based on the January 2010 Stocks & Commodities article by Donald Pendergast, “The Search for Your Trading Style.” In the article, Pendergast uses a trend-following system as an example of a trading style. The rules for the system are as follows:

1. Go long on the first 55-day “flat”-base breakout when volatility is falling during the base period
   (using a seven-day average true range [Atr]) and the Chaikin money flow indicator is rising over the base period;
2. Exit long positions using a 3 Atr trailing stop.

After testing with only the above rules, I found that the trailing stop didn’t work very well to protect profits, so I added a profit-protect stop that becomes active once the profit has reached 5%. I decided to protect 90% of the profit. I also set up a buy-stop entry, which uses the prior 55-day high for the entry level. I also added minimum price and volume filters ($5.00 and 300,000 average daily shares). I also ensured that the 3 Atr trailing stop could never exceed the 20% value by adding a 20% trailing stop. All exits are based on the closing price and then are exited at the next day’s opening price.

This is a long-only system that I tested, using my entire database for the period December 31, 1998, to January 8, 2010. In Figure 7, I show the equity curve and metrics for a portfolio-trading simulation. During this period, there were 2,145 signals generated, of which about half were actually traded in the portfolio simulation once capitalization rules were added. The large drawdown from July 2007 to March 2009 indicates that the system might benefit from the addition of some simple market timing.

Figure 7: AIQ SYSTEMS, FLAT-BASE BREAKOUT SYSTEM. Here is a sample equity curve for the flat-base breakout system trading a portfolio of up to 10 simultaneous positions together with the related metrics for the period December 31, 1998, to January 8, 2010.

The code can be downloaded from the Aiq website at www.aiqsystems.com and also from www.tradersedgesystems.com/traderstips.htm.

! FLAT BASE BREAKOUT
! From the article named “The Search for Your Trading Style”
! Author: Donald Pendergast, TASC January 2010
! Coded by: Richard Denning 1/09/10
! www.TradersEdgeSystems.com

! Use built-in stops:
  ! Trailing set to 80%
  ! Profit protect set to protect 90% over 5%
  ! Also use trailing ATR exit rule below “ExitLong”
! Pricing:
  ! Entry pricing - “user defined = EntryPr and Current”
  ! Exit pricing - “Default (Next Period Open)”

! INPUTS
baseLen is 55.
bsATR	is 5.
stpATR	is 3.
atrLen	is 7.
cmfLen	is 100.
minPrice	is 5.
minVme	is 3000. 
	
! ABBREVIATIONS:
C 	is [close].
C1 	is val([close],1).
O	is [open].	
H	is [high].
L	is [low].
Name	is description().
OSD	is offSetToDate(month(),day(),year()).
PD 	is {Position days}.

! AVERAGE TRUE RANGE
TR 	is Max(H - L,max(abs(C1 - L),abs(C1- H))). 
ATR	is simpleavg(TR,atrLen).
ATRpct	is simpleavg(TR / C,atrLen) * 100.

! BASE INDICATORS
HHbase	is highresult(H,baseLen,1).
HHdte	is scanany(H=^HHbase,baseLen+1).
HHos	is scanany(H=^HHbase,baseLen+1) then OSD.
LLbase	is lowresult(L,baseLen,1).
LLdte	is scanany(L=^LLbase,baseLen+1).
LLos	is scanany(L=^LLbase,baseLen+1) then OSD.
baseATR is (HHbase - LLbase) / ATR.
avgV	is simpleavg([volume],baseLen).

! CHAIKIN MONEY FLOW
AD	is [volume] * (C - O) / (H - L).
CMF	is sum(AD,cmfLen) / sum([volume],cmfLen).

! PRICE VOLUME AND DATA FILTER	
PVD	if C > minPrice and avgV > minVme 
	and hasdatafor(cmfLen+10) > baseLen.

! BREAKOUT RULE
BO	if H >  HHbase  and PVD.

! FLAT BASE RULE
FlatBase if (HHbase - LLbase) / ATR < bsATR and PVD.

! DECLINING VOLATILITY FILTER
VolaDwn	if slope2(ATR,baseLen) < 0 and PVD.

! INCREASING MONEYFLOW FILTER
MFup	if slope2(CMF,baseLen) > 0 and PVD.

! ENTRY RULE
Buy 	if  (HHbase - LLbase) / ATR < bsATR
	and H >  HHbase
	and slope2(ATR,baseLen) < 0
	and slope2(CMF,baseLen) > 0
	and PVD.

! ENTRY RULE RESTRICTED TO FIRST BREAK OUT IN LAST 10 BARS
FirstBUY if Buy and countof(BO,10) = 1.

! ENTRY PRICE
EntryPr	is max(O,HHbase).

! TRAILING EXIT
stop 	is L - ATR * stpATR.
stopVal	is highresult(stop,PD,1).
ExitLong if C < stopVal.

—Richard Denning
richard.denning@earthlink.net
for AIQ Systems

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TRADINGSOLUTIONS: EMPIRICAL MODE DECOMPOSITION

In “Empirical Mode Decomposition” in this issue, authors John Ehlers and Ric Way present a bandpass filter for use as a cycle- and trend-detection indicator.

These functions are described here and are also available as a function file that can be downloaded from the TradingSolutions website (www.tradingsolutions.com) in the “Free Systems” section.

Function Name: Ehlers Bandpass Filter Beta
Short Name: EBPF_Beta
Inputs: Period
Cos (Div (360, Period))

Function Name: Ehlers Bandpass Filter Gamma
Short Name: EBPF_Gamma
Inputs: Period, Delta
Div (1, Cos (Div (Mult (720, Delta), Period)))

Function Name: Ehlers Bandpass Filter Alpha
Short Name: EBPF_Alpha
Inputs: Period, Delta
Sub (EBPF_Gamma (Period, Delta), Sqrt (Sub (Pow (EBPF_Gamma (Period, Delta), 2), 1)))

Function Name: Ehlers Bandpass Filter
Short Name: EBPF
Inputs: Price, Period, Delta
Sub (Add (Mult (0.5, Mult (Sub (1, EBPF_Alpha (Period, Delta)), Sub (Price, Lag (Price, 2)))), Mult (Mult (EBPF_Beta (Period), Add (1, EBPF_Alpha (Period, Delta))), Prev (1))), Mult (EBPF_Alpha (Period, Delta), Prev (2)))

Function Name: Ehlers Bandpass Filter Trend
Short Name: EBPF_Trend
Inputs: Price, Period, Delta
Div (Add (MA (EBPF (Price, Period, Delta), Period), Lag (MA (EBPF (Price, Period, Delta), Period), Period)), 2)
Function Name: Ehlers Bandpass Filter Peak
Short Name: EBPF_Peak
Inputs: Price, Period, Delta
If (And (GT (Lag (EBPF (Price, Period, Delta), 1), EBPF (Price, Period, Delta)), GT (Lag (EBPF (Price, Period, Delta), 1), Lag (EBPF (Price, Period, Delta), 2))), Lag (EBPF (Price, Period, Delta), 1), Prev (1))

Function Name: Ehlers Bandpass Filter Valley
Short Name: EBPF_Valley
Inputs: Price, Period, Delta
If (And (LT (Lag (EBPF (Price, Period, Delta), 1), EBPF (Price, Period, Delta)), LT (Lag (EBPF (Price, Period, Delta), 1), Lag (EBPF (Price, Period, Delta), 2))), Lag (EBPF (Price, Period, Delta), 1), Prev (1))

Function Name: Ehlers Bandpass Filter Upper Threshold
Short Name: EBPF_Upper
Inputs: Price, Period, Delta, Fraction, Threshold Period
Mult (Fraction, MA (EBPF_Peak (Price, Period, Delta), Threshold Period))

Function Name: Ehlers Bandpass Filter Lower Threshold
Short Name: EBPF_Lower
Inputs: Price, Period, Delta, Fraction, Threshold Period
Mult (Fraction, MA (EBPF_Valley (Price, Period, Delta), Threshold Period))

—Gary Geniesse
NeuroDimension, Inc.
800 634-3327, 352 377-5144
www.tradingsolutions.com

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NINJATRADER: EMPIRICAL MODE DECOMPOSITION

The empirical mode decomposition indicator, discussed in “Empirical Mode Decomposition” by John Ehlers and Ric Way in this issue, has been implemented as an indicator available for download at www.ninjatrader.com/SC/March2010SC.zip.

Once it has been downloaded, from within the NinjaTrader Control Center window, select the menu File → Utilities → Import NinjaScript and select the downloaded file. This indicator is for NinjaTrader version 6.5 or greater.

You can review the indicator’s source code by selecting the menu Tools → Edit NinjaScript → Indicator from within the NinjaTrader Control Center window and selecting EmpiricalModeDecomposition.

NinjaScript indicators are compiled Dlls that run native, not interpreted, which provides you with the highest performance possible.

A sample chart implementing the strategy is shown in Figure 12.

Figure 12: NINJATRADER, Empirical Mode Decomposition. This screenshot shows the empirical mode decomposition indicator applied to a daily chart of Microsoft (MSFT).

—Raymond Deux & Austin Pivarnik
NinjaTrader, LLC
www.ninjatrader.com

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WAVE59: EMPIRICAL MODE DECOMPOSITION

In “Empirical Mode Decomposition” in this issue, authors John Ehlers and Ric Way present an objective method for determining whether the market is in trend mode or cycle mode.

Figure 14 is a daily chart of the Dow Jones Industrial Average showing their cycle indicator at work. We’ve enhanced their initial code to color the bars based on what mode the market is in: red means a downward-trending market, blue is an upward-trending market, and black is cycle mode. Notice how the recent upmove was built on a combination of blue upward-trending thrusts plus black cyclical retracements.

FIGURE 14: WAVE59, Empirical Mode Decomposition. The cycle indicator is shown here on a daily chart of the Dow Jones Industrial Average. Red indicates a downtrending market, blue an uptrending market, and black is cycle mode.

The following script implements this indicator in Wave59. As always, users of Wave59 can download these scripts directly using the QScript Library found at http://www.wave59.com/library.

Indicator:  Ehlers_EmpiricalModeDecomposition
input:price( (high+low)/2 ), period(20), delta(0.1), fraction(0.1), color(red), threshcolor(blue);
 
# initialization block 
if (barnum == barsback) {
    bp, peak, valley=0;
} 

#compute trend
beta = cos(360/period);
gamma = 1/cos(720*delta/period);   
alpha = gamma - sqrt(gamma*gamma - 1);   
bp=0.5*(1-alpha)*(price-price[2])  +  beta*(1+alpha)*bp[1]  -  alpha*bp[2];
mean=average(bp, 2*period);   
    
# compute thresholds  
peak = peak[1];
valley = valley[1];   
if (bp[1]>bp and bp[1]>bp[2]) peak = bp[1];
if (bp[1]<bp and bp[1]<bp[2]) valley = bp[1];
avgpeak = average(peak, 50);
avgvalley = average(valley, 50);
   
# plot it
plot1 = mean;       
color1 = color;       
plot2 = fraction*avgpeak;
plot3 = fraction*avgvalley; 
color2, color3 = threshcolor;
style2, style3 = ps_dot; 

# colorbars
if (mean>fraction*avgpeak) colorbar(barnum, blue, 1);
if (mean<fraction*avgvalley) colorbar(barnum, red, 1);

—Earik Beann
Wave59 Technologies Int’l, Inc.
www.wave59.com

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EASYLANGUAGE: EMPIRICAL MODE DECOMPOSITION — ARTICLE CODE

Below is the code from John Ehlers and Ric Way’s article in this issue, “Empirical Mode Decomposition.”

BANDPASS FILTER CODE IN EASYLANGUAGE
Inputs:	
	Price((H+L)/2),
	Period(20),
	delta(.1);

Vars:	
	gamma(0),
	alpha(0),
	beta(0),
	BP(0);

beta = Cosine(360 / Period);
gamma = 1 / Cosine(720*delta / Period);
alpha = gamma - SquareRoot(gamma*gamma - 1);
BP = .5*(1 - alpha)*(Price - Price[2]) + beta*(1 + alpha)*BP[1]- alpha*BP[2];

Plot1(BP);
Plot2(0);

EXTRACTING THE TREND IN EASYLANGUAGE
Inputs:	
	Price((H+L)/2),
	Period(20),
	Delta(.1);

Vars:	
	gamma(0),
	alpha(0),
	beta(0),
	BP(0),
	Trend(0);

beta = Cosine(360 / Period);
gamma = 1 / Cosine(720*delta / Period);
alpha = gamma - SquareRoot(gamma*gamma - 1);
BP = .5*(1 - alpha)*(Price - Price[2]) + beta*(1 + alpha)*BP[1] - alpha*BP[2];
Trend = Average(BP, 2*Period);

Plot1(Trend);
Plot2(0);


EMPIRICAL MODE DECOMPOSITION IN EASYLANGUAGE
Inputs:	
	Price((H+L)/2),
	Period(20),
	delta(.5),
	Fraction(.1);

Vars:	
	alpha(0),
	beta(0),
	gamma(0),
	BP(0),
	I(0),
	Mean(0),
	Peak(0),
	Valley(0),
	AvgPeak(0),
	AvgValley(0);

beta = Cosine(360 / Period);
gamma = 1 / Cosine(720*delta / Period);
alpha = gamma - SquareRoot(gamma*gamma - 1);
BP = .5*(1 - alpha)*(Price - Price[2]) + beta*(1 + alpha)*BP[1] - alpha*BP[2];
Mean = Average(BP, 2*Period);
Peak = Peak[1];
Valley = Valley[1];
If BP[1] > BP and BP[1] > BP[2] Then Peak = BP[1];
If BP[1] < BP and BP[1] < BP[2] Then Valley = BP[1];

AvgPeak = Average(Peak, 50);
AvgValley = Average(Valley, 50);

Plot1(Mean);
Plot2(Fraction*AvgPeak);
Plot6(Fraction*AvgValley);

—John Ehlers
www.isignals.com
—Ric Way
ricway@taosgroup.org.

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