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

This is a different and earlier version of the **Sinewave Indicator**, from what is described in John Ehlers’ books *Rocket Science for Traders* (2001-07-20) and *Cybernetic Analysis for Stocks and Futures* (2004-03-29). However, this is the most popular version of the algorithm and seems to achieve better results.

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// The Sinewave Indicator // 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 = 0.635 Qmult = 0.338 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 and Quadrature > 0 then Phase = 180 - Phase Endif If InPhase < 0 and Quadrature < 0 then Phase = 180 + Phase Endif If InPhase > 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] < 90 and Phase > 270 then DeltaPhase = 360 + Phase[1] - Phase Endif If DeltaPhase < 1 then DeltaPhase = 1 Endif If DeltaPhase > 60 then DeltaPhase = 60 Endif // Sum DeltaPhases to reach 360 degrees. The sum is the instantaneous period. InstPeriod = 0 Value4 = 0 For count = 0 to 40 do Value4 = Value4 + DeltaPhase[count] If Value4 > 360 and InstPeriod = 0 then InstPeriod = count Endif Next // Resolve Instantaneous Period errors and smooth If InstPeriod = 0 then InstPeriod = InstPeriod[1] Endif Value5 = .25*InstPeriod + .75*Value5[1] // Compute Dominant Cycle Phase, Sine of the Phase Angle, and Leadsine Period = ROUND(Value5) RealPart = 0 ImagPart = 0 For count = 0 to Period - 1 RealPart = RealPart + SIN(360 * count / Period) * (Price[count]) ImagPart = ImagPart + COS(360 * count / Period) * (Price[count]) Next If ABS(ImagPart) > 0.001 then DCPhase = ATAN(RealPart / ImagPart) Endif If ABS(ImagPart) <= 0.001 then DCPhase = 90 * SGN(RealPart) Endif DCPhase = DCPhase + 90 If ImagPart < 0 then DCPhase = DCPhase + 180 Endif If DCPhase > 315 then DCPhase = DCPhase - 360 Endif Endif Return Sin(DCPhase) as "Sine", Sin(DCPhase+45) as "LeadSine" |

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:

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If BarIndex > 5 then // Compute InPhase and Quadrature components Value1 = Price - Price[6] Value2 = Value1[3] Value3 = .75*(Value1 - Value1[6]) + .25*(Value1[2] - Value1[4]) InPhase = .33*Value2 + .67*InPhase[1] Quadrature = .2*Value3 + .8*Quadrature[1] |

The attached screenshot shows the **Sinewave Indicator** using original description (top) of and the alternative Hilbert Transform formula (bottom).

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cbeukes• 355 days ago #Very interesting indicator. Any advice on identifying the transition between ranging and trending markets?

Horance• 355 days ago #This is a good question. John Ehlers explains it in Rocket Science for Traders. You have to use the Sinewave Indicator in conjunction with the Instantaneous Trendline (https://www.prorealcode.com/prorealtime-indicators/john-ehlers-instantaneous-trendline/). Basically, when the trendline crosses the Kalman filter, we start to count the number of bars. While the number of bars is inferior to half a period, we stay in cycle mode, otherwise we enter trend mode.

cbeukes• 352 days ago #Much appreciated, I will give that a try. Also, is there any criteria that one could use to identify whether if a sinewave cycle cross is valid? Perhaps the level of an RSI or Stochastic using the cycle period as calculated above?

firemyst• 129 days ago #Thanks for the code! I’m trying to understand how it works, and have a few questions… lines 16 & 17: howdoes InPhase[3] and Quadrature[2] have any values? Any indexes below 6 aren’t assigned. So, those values just return zero? Same with the Value3[4] array. What value does Value3[4] have from 4 bars ago? High? Low? Close? Nothing?

Thank you 🙂