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/
Skrip sumber terbuka
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Untuk akses pantas pada carta, tambah skrip ini kepada kegemaran anda — ketahui lebih lanjut di sini.
VIP Membership Info: patreon.com/algxtrading/membership
Penafian
Skrip sumber terbuka
Dalam semangat sebenar TradingView, pencipta skrip ini telah menjadikannya sumber terbuka supaya pedagang dapat menilai dan mengesahkan kefungsiannya. Terima kasih kepada penulis! Walaupun anda boleh menggunakannya secara percuma, ingat bahawa menerbitkan semula kod ini adalah tertakluk kepada Peraturan Dalaman kami.
Untuk akses pantas pada carta, tambah skrip ini kepada kegemaran anda — ketahui lebih lanjut di sini.
VIP Membership Info: patreon.com/algxtrading/membership