FourierSeriesModel
Synthesized market model using fundamental and harmonic frequency components.
Usage
Use to model price as a sum of sine wave harmonics for short-term prediction. Most effective in clearly cyclical markets; combine with a cycle mode detector to disable it in trends.
Background
The Fourier Series Model fits harmonically related sine waves to recent price history using least-squares coefficients. Ehlers shows that projecting this model one bar forward gives a price forecast useful for anticipatory entry timing at predicted cycle turns.
Parameters
fundamental(default: 20): Fundamental cycle period
Formula
[ BP_k = \text{BandPass}(Price, Fundamental/k) ] [ Q_k = \frac{Fundamental}{2\pi} (BP_{k} - BP_{k,t-1}) ] [ P_k = \sum_{n=0}^{F-1} (BP_{k,t-n}^2 + Q_{k,t-n}^2) ] [ Wave = BP_1 + \sqrt{P_2/P_1}BP_2 + \sqrt{P_3/P_1}BP_3 ]