T3 Average

T3Avg.efs  
EFSLibrary - Discussion Board  

File Name: T3Avg.efs

Description:
T3 Average

Formula Parameters:

• Length: 5
• Price Data To Use: Close

Notes:
This indicator plots the moving average described in the January, 1998 issue of S&C, p.57, "Smoothing Techniques for More Accurate Signals", by Tim Tillson. This indicator plots T3 moving average presented in Figure 4 in the article. T3 indicator is a moving average which is calculated according to formula:

T3(n) = GD(GD(GD(n))), 

where GD - generalized DEMA (Double EMA) and calculating according to this:

GD(n,v) = EMA(n) * (1+v)-EMA(EMA(n)) * v,

where "v" is volume factor, which determines how hot the moving averageRs response to linear trends will be. The author advises to use v=0.7.
When v = 0, GD = EMA, and when v = 1, GD = DEMA. In between, GD is a less aggressive version of DEMA. By using a value for v less than1, trader cure the multiple DEMA overshoot problem but at the cost of accepting some additional phase delay.
In filter theory terminology, T3 is a six-pole nonlinear Kalman filter. Kalman filters are ones that use the error W in this case, (time series - EMA(n)) W to correct themselves. In the realm of technical analysis, these are called adaptive moving averages; they track the time series more aggres-sively when it is making large moves. Tim Tillson is a software project manager at Hewlett-Packard, with degrees in
mathematics and computer science. He has privately traded options and equities for 15 years.

Download File:
T3Avg.efs


EFS Code:

/*********************************
Provided By:  
    eSignal (Copyright c eSignal), a division of Interactive Data 
    Corporation. 2008. 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:        
   T3 Average 

Version:            1.0  09/24/2008

Notes:
    This indicator plots the moving average described in the January, 1998 issue
    of S&C, p.57, "Smoothing Techniques for More Accurate Signals", by Tim Tillson.
    This indicator plots T3 moving average presented in Figure 4 in the article.
    T3 indicator is a moving average which is calculated according to formula:
        T3(n) = GD(GD(GD(n))),
    where GD - generalized DEMA (Double EMA) and calculating according to this:
        GD(n,v) = EMA(n) * (1+v)-EMA(EMA(n)) * v,
    where "v" is volume factor, which determines how hot the moving average’s response
    to linear trends will be. The author advises to use v=0.7.
    When v = 0, GD = EMA, and when v = 1, GD = DEMA. In between, GD is a less aggressive
    version of DEMA. By using a value for v less than1, trader cure the multiple DEMA
    overshoot problem but at the cost of accepting some additional phase delay.
    In filter theory terminology, T3 is a six-pole nonlinear Kalman filter. Kalman
    filters are ones that use the error — in this case, (time series - EMA(n)) — 
    to correct themselves. In the realm of technical analysis, these are called adaptive
    moving averages; they track the time series more aggres-sively when it is making large
    moves. Tim Tillson is a software project manager at Hewlett-Packard, with degrees in
    mathematics and computer science. He has privately traded options and equities for 15 years.    

Formula Parameters:                     Default:
    Length                                  5
    Price Data To Use                      Close
**********************************/

var fpArray = new Array();
var bInit = false;

function preMain() {

    setPriceStudy(true);
    setStudyTitle("T3");
    setCursorLabelName("Slope", 0);
   
    setDefaultBarFgColor(Color.blue, 0);

    var x=0;
    fpArray[x] = new FunctionParameter("Length", FunctionParameter.NUMBER);
    with(fpArray[x++]){
        setLowerLimit(1);        
        setDefault(5);
    }

    fpArray[x] = new FunctionParameter("Price", FunctionParameter.STRING);
    with(fpArray[x++]){
        setName("Price Data To Use");
        addOption("open"); 
        addOption("high");
        addOption("low");
        addOption("close");
        addOption("hl2");
        addOption("hlc3");
        addOption("ohlc4"); 
        setDefault("close"); 
    }
}

var xe1 = null;
var xe2 = null;
var xe3 = null;
var xe4 = null;
var xe5 = null;
var xe6 = null;
var xMyPrice = null;
var nT3Average = 0;

function main(Price, Length) {
var nState = getBarState();

    if (nState == BARSTATE_ALLBARS) {
        if (Price == null) Price = "close";
        if (Length == null) Length = 5;
    }    

    if ( bInit == false ) { 
        xMyPrice = eval(Price)();
        xe1 = ema(Length, xMyPrice);
        xe2 = ema(Length, xe1);
        xe3 = ema(Length, xe2);        
        xe4 = ema(Length, xe3);        
        xe5 = ema(Length, xe4);        
        xe6 = ema(Length, xe5);                
        bInit = true; 
    } 

    if (xe1.getValue(0) == null || xe2.getValue(0) == null || xe3.getValue(0) == null ||
        xe4.getValue(0) == null || xe5.getValue(0) == null || xe6.getValue(0) == null) return;

    var b = 0.7;
    var c1 = -b*b*b;
    var c2 = 3*b*b+3*b*b*b;
    var c3 = -6*b*b-3*b-3*b*b*b;
    var c4 = 1+3*b+b*b*b+3*b*b;

    nT3Average = c1 * xe6.getValue(0) + c2 * xe5.getValue(0) + c3 * xe4.getValue(0) + c4 * xe3.getValue(0);

    return nT3Average;
}