This implements the Even Better Sinewave indicator as described in the book Cycle Analysis for Traders by John F. Ehlers.
In the example I used 36 as the cycle to be analyzed and a second cycle with a shorter period, 9, the larger period tells where the dominant cycle is heading, and the faster cycle signals entry/exit points and reversals.
In the example I used 36 as the cycle to be analyzed and a second cycle with a shorter period, 9, the larger period tells where the dominant cycle is heading, and the faster cycle signals entry/exit points and reversals.
// Madrid : 09/Jun/2015 21:09 : Even Better Sinewave : 1.0
// This implements the Even Better Sinewave indicator
// Ref. Cycle Analysis for Traders by John F. Ehlers.
//
study("Madrid Sinewave", shorttitle="MSineWave")
Duration = input(36)
src = close
OB = 0.85, OS = -0.85
PI = 3.14159265358979
deg2rad( deg ) =>
deg*PI/180.0
lowerBand = input(9)
ssFilter( price, lowerBand ) =>
angle = sqrt(2)*PI/lowerBand
a1= exp(-angle)
b1 = 2*a1*cos(angle)
c2 = b1
c3 = -a1*a1
c1 = 1 - c2 -c3
filt = c1*(price + nz(price[1]))/2 + c2*nz(filt[1]) + c3*nz(filt[2])
// HighPass filter cyclic components whose periods are shorter than Duration input
x = src
angle = deg2rad(360)/Duration
alpha1 = ( 1-sin(angle) ) / cos(angle)
HP = 0.5*(1+alpha1)*(x-x[1]) + alpha1*nz(HP[1],0)
// Smooth with a Super Smoother Filter
Filt = ssFilter( HP, lowerBand )
Wave = ( Filt + nz(Filt[1],0) + nz(Filt[2],0) ) / 3
Pwr = ( Filt*Filt + nz(Filt[1],0)* nz(Filt[1],0) + nz(Filt[2],0)* nz(Filt[2],0) ) /3
// Normalize the Average Wave to Square Root of the Average Power
sineWave = Wave / sqrt(Pwr)
// Output
sineWaveColor = sineWave>OB?green
: sineWave<OS?red
: change(sineWave)>0?green
: red
plot( sineWave, color=sineWaveColor, linewidth=3 )
plot( sineWave, color=sineWaveColor, linewidth=1, style=histogram )
hline(0, color=silver, linestyle=dotted)