Fourier Extrapolation of Variety Moving Averages [Loxx]

Fourier Extrapolation using the Quinn-Fernandes algorithm is one of several (5-10) methods of signals forecasting that I'l be demonstrating in Pine Script.
What is Fourier Extrapolation?
This indicator uses a multi-harmonic (or multi-tone) trigonometric model of a price series xi, i=1..n, is given by:
xi = m + Sum( a*Cos(w*i) + b*Sin(w*i), h=1..H )
Where:
xi - past price at i-th bar, total n past prices;
m - bias;
a and b - scaling coefficients of harmonics;
w - frequency of a harmonic ;
h - harmonic number;
H - total number of fitted harmonics.
Fitting this model means finding m, a, b, and w that make the modeled values to be close to real values. Finding the harmonic frequencies w 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.
see here: A Fast Efficient Technique for the Estimation of Frequency , B. G. Quinn and J. M. Fernandes, Biometrika, Vol. 78, No. 3 (Sep., 1991), pp . 489-497 (9 pages) Published By: Oxford University Press
The indicator has the following input parameters:
src - input source
npast - number of past bars, to which trigonometric series is fitted;
Nfut - number of predicted future bars;
nharm - total number of harmonics in model;
frqtol - tolerance of frequency calculations.
Included:
- Loxx's Expanded Source Types
- Loxx's Moving Averages
Other indicators using this same method
Fourier Extrapolator of Variety RSI w/ Bollinger Bands [Loxx]
https://www.tradingview.com/script/pHlxm005-Fourier-Extrapolator-of-Variety-RSI-w-Bollinger-Bands-Loxx/
Fourier Extrapolator of Price w/ Projection Forecast
https://www.tradingview.com/script/u0r2gpti-Fourier-Extrapolator-of-Price-w-Projection-Forecast-Loxx/
Fourier Extrapolator of Price
https://www.tradingview.com/script/8gqRTSRR-Fourier-Extrapolator-of-Price-Loxx/
Loxx's Moving Averages: Detailed explanation of moving averages inside this indicator
https://www.tradingview.com/script/x6otWKAc-Moving-Average-Filters-Add-on-w-Expanded-Source-Types-Loxx/
Loxx's Expanded Source Types: Detailed explanation of source types used in this indicator
https://www.tradingview.com/script/AdBj6Sva-Better-Heiken-Ashi-Candles-w-Expanded-Source-Types-Loxx/
Script open-source
In pieno spirito TradingView, il creatore di questo script lo ha reso open-source, in modo che i trader possano esaminarlo e verificarne la funzionalità. Complimenti all'autore! Sebbene sia possibile utilizzarlo gratuitamente, ricorda che la ripubblicazione del codice è soggetta al nostro Regolamento.
Per un accesso rapido a un grafico, aggiungi questo script ai tuoi preferiti: per saperne di più clicca qui.
VIP Membership Info: patreon.com/algxtrading/membership
Declinazione di responsabilità
Script open-source
In pieno spirito TradingView, il creatore di questo script lo ha reso open-source, in modo che i trader possano esaminarlo e verificarne la funzionalità. Complimenti all'autore! Sebbene sia possibile utilizzarlo gratuitamente, ricorda che la ripubblicazione del codice è soggetta al nostro Regolamento.
Per un accesso rapido a un grafico, aggiungi questo script ai tuoi preferiti: per saperne di più clicca qui.
VIP Membership Info: patreon.com/algxtrading/membership