Fourier transform for stock price forecasting

External question — Quantitative Finance Stack Exchange Author: lazarea Original post: https://quant.stackexchange.com/questions/61565 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. I am trying to forecast stock prices using Fast Fourier Transform, and plot historical, "future" (i.e. real) and forecast prices on the same chart to visually compare the accuracy of the forecasting method. However, I am puzzled as to why the output forecast values are much lower than the last input data of the time series itself. import numpy as np import pylab as pl from numpy import fft from pandas_datareader import data def fourierExtrapolation(x, n_predict): n = x.size n_harm = 50 t = np.arange(0, n) p = np.polyfit(t, x, 1) x_notrend = x - p[0] * t x_freqdom = fft.fft(x_notrend) f = fft.fftfreq(n) indexes = list(range(n)) indexes.sort(key=lambda i: np.absolute(f[i])) t = np.arange(0, n + n_predict) restored_sig = np.zeros(t.size) for i in indexes[:1 + n_harm * 2]: ampli = np.absolute(x_freqdom[i]) / n phase = np.angle(x_freqdom[i]) restored_sig += ampli * np.cos(2 * np.pi * f[i] * t + phase) return restored_sig + p[0] * t df = data.DataReader('AAPL', 'yahoo', '2017-01-01', '2021-02-28') hist_prices = df.loc[:'2020-11-01','Adj Close'] fut_prices = df.loc['2020-11-01':,'Adj Close'] extrapolation = fourierExtrapolation(hist_prices, len(fut_prices)-len(hist_prices)) Now when I print the extrapolated values, they are very low compared to hist_prices and fut_prices which becomes very apparent by running the below code: pl.plot(fut_prices.index, extrapolation, 'r', label='extrapolation') pl.plot(hist_prices.index, hist_prices, 'b', label='x_hist', linewidth=1) pl.plot(fut_prices.index, fut_prices, 'g', label='x_real', linewidth=1) pl.legend() pl.show() What am I missing? Why isn't my forecast series in the same order of magnitude with the input prices?

External answer — Quantitative Finance Stack Exchange Author: Sergei Rodionov Original post: https://quant.stackexchange.com/a/61577 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. Here's a working example for python3. import numpy as np import pylab as pl from numpy import fft from datetime import datetime from pandas_datareader import data as pdr """ https://gist.github.com/tartakynov/83f3cd8f44208a1856ce """ def fourierExtrapolation(x, n_predict): n = x.size n_harm = 50 t = np.arange(0, n) p = np.polyfit(t, x, 1) x_notrend = x - p[0] * t x_freqdom = fft.fft(x_notrend) f = fft.fftfreq(n) indexes = list(range(n)) indexes.sort(key=lambda i: np.absolute(f[i])) #indexes.sort(key=lambda i: np.absolute(x_freqdom[i])) #indexes.reverse() t = np.arange(0, n + n_predict) restored_sig = np.zeros(t.size) for i in indexes[:1 + n_harm * 2]: ampli = np.absolute(x_freqdom[i]) / n phase = np.angle(x_freqdom[i]) restored_sig += ampli * np.cos(2 * np.pi * f[i] * t + phase) return restored_sig + p[0] * t data = pdr.get_data_yahoo('AAPL', datetime(2017, 1, 1), datetime(2022, 1, 1)) hist = data.loc[:,'Adj Close'].values train = data.loc[:'2020-11-01','Adj Close'].values n_predict = len(hist) - len(train) extrapolation = fourierExtrapolation(train, n_predict) pl.plot(np.arange(0, hist.size), hist, 'b', label = 'Data', linewidth = 3) pl.plot(np.arange(0, train.size), train, 'c', label = 'Train', linewidth = 2) pl.plot(np.arange(0, extrapolation.size), extrapolation, 'r', label = 'Predict', linewidth = 1) pl.legend() pl.show()

External answer — Quantitative Finance Stack Exchange Author: qwertydotplus Original post: https://quant.stackexchange.com/a/85850 License: CC BY-SA 4.0 — https://creativecommons.org/licenses/by-sa/4.0/ Adaptation: HTML converted to plain text; contact email addresses removed. because the Fourier Transform takes as input one period of a periodic waveform, thus an extrapolation from any modification of the FT will "try to be" periodic with a period equal to your input data (the "extrapolation" will end up being approximately a shifted copy of your input regardless of how you massage the data). you should read up on how the FT works and try to make your model look further into the future. your "extrapolation" will almost certainly better match the "training" data than the future data.