Ehlers Early Onset Trend

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In his article in this issue, “The Quotient             Transform,” author John Ehlers introduces the quotient             transform (QT), a zero-lag filter that can be used for the purpose of timely trend detection. The QT is an advancement of the technique he presented in his January 2014 S&C article, “Predictive And Successful Indicators.” This time, the output of a roofing filter (which includes applying a high-pass filter and SuperSmoother filter) is normalized.
Code and other platforms
Pinescript code Glaz and LazyBear
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//By Glaz and LazyBear
study(title="Ehlers Early Onset Trend",shorttitle="EOT")

Quotient(LPPeriod, K)=>
    PI = 3.1415926
    angle = 0.707 * 2 * PI / 100
    alpha1 = ( cos( angle ) + sin( angle ) - 1 ) / cos( angle )

    a1 = exp( -1.414 * PI / LPPeriod )
    b1 = 2 * a1 * cos( 1.414 * PI / LPPeriod )
    c2 = b1
    c3 = -a1 * a1
    c1 = 1 - c2 - c3

    HP= pow((1-alpha1/2),2)*(close - (2*close[1]) + close[2]) + 2*(1-alpha1)*nz(HP[1]) - pow((1-alpha1),2)* nz(HP[2])
    Filt= c1 * (HP + nz(HP[1]))/2 + c2*nz(Filt[1]) + c3*nz(Filt[2])
    Pk= iff(abs(Filt) >  0.991 *nz(Pk[1]), abs(Filt), 0.991 * nz(Pk[1]))
    X = nz(Filt / Pk)
    q=( X + K ) / ( K * X + 1 ) 

plot(Quotient( Period, Q1 ),color=red) 
plot(Quotient( Period, Q2 ),color=aqua)
This indicator looked good on first impression. But it failed my test. I dislike indicators which show strong divergences against the actual price in the wrong direction for far too long. In this case a buy signal for Bitcoin from November to December 2014, while the price was actually falling down. Below is a screenshot with default settings (and you can fine-tune the QT to also show a zero line buy crossing there). The QT is behaving with divergences like the MACD in that area.

So be aware if you use this indicator that you use other indicators in combination which don't show (strong) divergences. Being faster than most it is overall one of the better indicators around. Thank you both Glaz and LazyBear for coding and sharing it.


P.S. And if the divergence of the red line plays out we have a documented screenshot of the Bitcoin price breakout to the upside, which would end the one year downtrend :)
ChartArt ChartArt
Here is the 3-month / quarterly Bitcoin price trend on a log scale chart (also showing the divergence to buy here in February 2015, which I think is true):

ChartArt ChartArt