Fourier Extrapolation in Python

fourex.py

import numpy as np
import pylab as pl
from numpy import fft
    
def fourierExtrapolation(x, n_predict):
    n = x.size
    n_harm = 10                     # number of harmonics in model
    t = np.arange(0, n)
    p = np.polyfit(t, x, 1)         # find linear trend in x
    x_notrend = x - p[0] * t        # detrended x
    x_freqdom = fft.fft(x_notrend)  # detrended x in frequency domain
    f = fft.fftfreq(n)              # frequencies
    indexes = range(n)
    # sort indexes by frequency, lower -> higher
    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   # amplitude
        phase = np.angle(x_freqdom[i])          # phase
        restored_sig += ampli * np.cos(2 * np.pi * f[i] * t + phase)
    return restored_sig + p[0] * t
    
def main():
    x = np.array([669, 592, 664, 1005, 699, 401, 646, 472, 598, 681, 1126, 1260, 562, 491, 714, 530, 521, 687, 776, 802, 499, 536, 871, 801, 965, 768, 381, 497, 458, 699, 549, 427, 358, 219, 635, 756, 775, 969, 598, 630, 649, 722, 835, 812, 724, 966, 778, 584, 697, 737, 777, 1059, 1218, 848, 713, 884, 879, 1056, 1273, 1848, 780, 1206, 1404, 1444, 1412, 1493, 1576, 1178, 836, 1087, 1101, 1082, 775, 698, 620, 651, 731, 906, 958, 1039, 1105, 620, 576, 707, 888, 1052, 1072, 1357, 768, 986, 816, 889, 973, 983, 1351, 1266, 1053, 1879, 2085, 2419, 1880, 2045, 2212, 1491, 1378, 1524, 1231, 1577, 2459, 1848, 1506, 1589, 1386, 1111, 1180, 1075, 1595, 1309, 2092, 1846, 2321, 2036, 3587, 1637, 1416, 1432, 1110, 1135, 1233, 1439, 894, 628, 967, 1176, 1069, 1193, 1771, 1199, 888, 1155, 1254, 1403, 1502, 1692, 1187, 1110, 1382, 1808, 2039, 1810, 1819, 1408, 803, 1568, 1227, 1270, 1268, 1535, 873, 1006, 1328, 1733, 1352, 1906, 2029, 1734, 1314, 1810, 1540, 1958, 1420, 1530, 1126, 721, 771, 874, 997, 1186, 1415, 973, 1146, 1147, 1079, 3854, 3407, 2257, 1200, 734, 1051, 1030, 1370, 2422, 1531, 1062, 530, 1030, 1061, 1249, 2080, 2251, 1190, 756, 1161, 1053, 1063, 932, 1604, 1130, 744, 930, 948, 1107, 1161, 1194, 1366, 1155, 785, 602, 903, 1142, 1410, 1256, 742, 985, 1037, 1067, 1196, 1412, 1127, 779, 911, 989, 946, 888, 1349, 1124, 761, 994, 1068, 971, 1157, 1558, 1223, 782, 2790, 1835, 1444, 1098, 1399, 1255, 950, 1110, 1345, 1224, 1092, 1446, 1210, 1122, 1259, 1181, 1035, 1325, 1481, 1278, 769, 911, 876, 877, 950, 1383, 980, 705, 888, 877, 638, 1065, 1142, 1090, 1316, 1270, 1048, 1256, 1009, 1175, 1176, 870, 856, 860])
    n_predict = 100
    extrapolation = fourierExtrapolation(x, n_predict)
    pl.plot(np.arange(0, extrapolation.size), extrapolation, 'r', label = 'extrapolation')
    pl.plot(np.arange(0, x.size), x, 'b', label = 'x', linewidth = 3)
    pl.legend()
    pl.show()
    
if __name__ == "__main__":
    main()

@DanielPark827
Sorting the largest amplitude will give you a better frequency selection because the amplitude in the frequency domain indicates how much each frequency contributes to the value of the original data. So selecting larger amplitudes will give you frequencies that predict more of the pattern in your data.