Fourier extrapolation of price - indicator for MetaTrader 5

A multi-harmonic (or multi-tone) trigonometric model of a price series x[i], i=1..n, is given by:

where:

• x[i] - past price at i-th bar, total n past prices;
• m - bias;
• a[h] and b[h] - scaling coefficients of harmonics;
• w[h] - frequency of a harmonic;
• h - harmonic number;
• H - total number of fitted harmonics.

Fitting this model means finding m, a[h], b[h], and w[h] that make the modeled values to be close to real values. Finding the harmonic frequencies w[h] is the most difficult part of fitting a trigonometric model. In the case of a Fourier series, these frequencies are set at 2*pi*h/n. But, the Fourier series extrapolation means simply repeating the n past prices into the future.

This indicator uses the Quinn-Fernandes algorithm to find the harmonic frequencies. It fits harmonics of the trigonometric series one by one until the specified total number of harmonics H is reached. After fitting a new harmonic, the coded algorithm computes the residue between the updated model and the real values and fits a new harmonic to the residue.

The indicator has the following input parameters:

• Npast - number of past bars, to which trigonometric series is fitted;
• Nfut - number of predicted future bars;
• Nharm - total number of harmonics in model;
• FreqTOL - tolerance of frequency calculations.
  

The indicator plots two curves: the blue curve indicates modeled past values and the red curve indicates the modeled future values.