This adaptive version applies the concept described by John Ehlers in the book Rocket Science for traders, for making standard indicators adaptive. The indicator uses the homodyne descriminator to compute the dominant cycle. To apply the homodyne descriminator, real and imaginary parts have to be calculated from the Inphase and Quadrature components. (Inphase and Quadrature components are deduced using the Hilbert transform. To learn more about this, read the article on Advanced adaptive Indicators theory and implementation. The sections on Complex numbers and phasors for measuring market cycles and also Measuring cycle period).
To achieve this, the product of the current Inphase component and its value a bar ago are added to the product of the current Quadrature component and its value one bar ago to produce the real part. For the imaginary part, the product of the current Quadrature component and the value of Inphase component a bar ago is taken away from the product of the current Inphase component and the value of the Quadrature component a bar ago. Both real and imaginary parts are then smoothed, before the cycle period can be calculated.
The cycle is calculated by taking the arctangent of the imaginary part divided by the real part. Restrictions are placed so as to make sure that the rate of change of the cycle period is limited to +-50% of the previous cycle period and further more, the resulting cycle period is limited to being greater than 6 and less than 50. Smoothing is then applied for the last time on the cycle period.
This cycle period value is then used at each bar close as the value that represents the number of bars back to be analyzed for producing the Bollinger bands indicator. This enables the adaptive nature of the indicator.
- The limits value controls the number of bars the indicator will be drawn for .
- Deviation is decimal value that denotes the standard deviation. The lower the number, the narrower the bands of the indicator will be.