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  • T3 Average

    /*********************************
    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;
    }
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