John Ehlers Instantaneous Trendline

John Ehlers Instantaneous Trendline

This is an implementation of John Ehlers’ Instantaneous Trendline, as described in Market Mode Strategies (1999-10-19).

The code has been slightly enhanced to return a Zero Lag exponential moving average, like it was done here.

A more recent formula of Hilbert Transform, described in Squelch those Whipsaws (2000-24-03), can be used, by replacing the beginning of the code with:

The attached screenshot shows the Instantaneous Trendline using original description (top) of and the alternative Hilbert Transform formula (bottom).

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  1. Nicolas • 08/27/2018 #

    Thanks a lot for this new valuable addition to our library. I changed line 76 with “barindex” instead of “currentbar”.

  2. Horance • 08/27/2018 #

    Thanks. I’ve noticed this leftover after submission, but it was too late for editing. BTW, I think it would be nice to add the ability to edit our own posts.

  3. Etienne • 300 days ago #

    Thanks Horance for porting this code to PRT.
    I would like to bring some speedup to your code. I’ve been willing to use it some strategies, but the computation time is disastrous when backtesting.
    I optimized some parts of the code. The resulting figures are unchanged, but it the code is 4 time quicker to compute.

    I did 2 optimizations :
    1/ sum of deltaPhases can be computed more quickly if you observe that the current InstPeriod is close to the previous one. (which by the way is functionaly quite intutive).
    Therefore, we reuse the previous InstPeriod to compute the summation[InstPeriod](DeltaPhase) .Then we check if we went above or below 360, then we adjust the current InstPeriod with a few loops…
    On my machine, the code is twice faster on this part…

    2/ averaging using the calculated period
    In PRT, loops are slow, very slow. We are much better off, if we use native function like average…
    The gain in speedup is approx a ratio of 4 on this part…

    I’m providing the full code below.
    Thanks again

    // Instantaneous Trendline
    // Market Mode Strategies
    // 1999-10-19 John F. Ehlers
    // http://www.jamesgoulding.com/Research_II/Ehlers/Ehlers%20(Market%20Mode%20Strategies).doc

    Price = (high+low)/2
    Imult = .635
    Qmult = .338

    If BarIndex > 6 then

    // Detrend Price
    Value3 = Price – Price[7]

    // Compute InPhase and Quadrature components
    Inphase = 1.25*(Value3[4] – Imult*Value3[2]) + Imult*InPhase[3]
    Quadrature = Value3[2] – Qmult*Value3 + Qmult*Quadrature[2]

    // Use ArcTangent to compute the current phase
    If ABS(InPhase + InPhase[1]) > 0 then
    a = ABS((Quadrature+Quadrature[1]) / (InPhase+InPhase[1]))
    Phase = ATAN(a)
    Endif

    // Resolve the ArcTangent ambiguity
    If InPhase 0 then
    Phase = 180 – Phase
    Endif
    If InPhase < 0 and Quadrature 0 and Quadrature < 0 then
    Phase = 360 – Phase
    Endif

    // Compute a differential phase, resolve phase wraparound, and limit delta phase errors
    DeltaPhase = Phase[1] – Phase
    If Phase[1] 270 then
    DeltaPhase = 360 + Phase[1] – Phase
    Endif
    If DeltaPhase 60 then
    DeltaPhase = 60
    Endif

    // Sum DeltaPhases to reach 360 degrees. The sum is the instantaneous period.
    InstPeriod = InstPeriod[1]+1
    Value4 = summation[InstPeriod](DeltaPhase)
    if Value4 360 then
    if Value4 > 360 then
    while Value4 > 360 do
    InstPeriod = InstPeriod -1
    Value4 = Value4 – DeltaPhase[InstPeriod]
    wend
    else
    while Value4 < 360 do
    Value4 = Value4 + DeltaPhase[InstPeriod]
    InstPeriod = InstPeriod + 1
    wend
    InstPeriod = InstPeriod -1
    endif
    endif

    // Resolve Instantaneous Period errors and smooth
    If InstPeriod = 0 then
    InstPeriod = InstPeriod[1]
    Endif
    SmoothPeriod = .25*InstPeriod + .75*SmoothPeriod[1]

    // Compute Trendline as simple average over the measured dominant cycle period
    Period = ROUND(SmoothPeriod)
    Trendline= average [Period + 2](Price)

    Value11 = .33*(Price + .5*(Price – Price[3])) + .67*Value11[1]

    If barindex < 26 then
    Trendline = Price
    Value11 = Price
    Endif

    Endif

    Return Trendline as "TR", Value11 as "ZL"

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