How can I convert FFT results for real-world times series analysis?

Question

I have a dataset containing the daily sum of news articles for specific topics since 1995 (for this example, I'm trying to analyze the topic "Soccer, Football"). I am trying to use the fast fourier transform (fft) but am not sure how to interpret the results. How am I supposed to convert the frequency to a daily scale?

from scipy.fftpack import fft
N = 8335 # lenth of times series (days)
# Nyquist Sampling Criteria
T = 1/8335 # inverse of the sampling rate
x = np.linspace(0.0, 1.0/(2.0*T), int(N/2))

# FFT algorithm
yr = fft(array) # "raw" FFT with both + and - frequencies
y = 2/N * np.abs(yr[0:np.int(N/2)]) # positive freqs only

# Plotting the results
plt.plot(x, y)
plt.figsize=(25,10)
plt.ylim(0,.08)
plt.xlabel('Frequency (Hz)')
plt.ylabel('Vibration (g)')
plt.title('Soccer,Football');

The results: See here 3 spikes in the power spectrum but in audio frequency terms

How can I convert the three frequencies to understand the lengths of the cycles in days?

Tried @Prieur Julien's solution - I'm not quite sure what is the output this gave me. I have an array with n values (in this case one per each day), with the values rising up to 4.999, only to fall to -4.999 and then rise again to end at 0... what is the significance of these values? — Dror M, Sep 18 '19 at 14:31
Since the signal is of length 8335 days, its period for the DFT is 8335 days. Hence the frequency of bin 1 is 1 per 8335 days, or 1/8335 day^-1. The second bin is 2/8335 and so on. For instance, the week period (1/7 days^-1) is near the bin 8335/7=1190, the month period is near the bin 8335/30=278. Hence the small first, the second peak and third peak conrespond to monthly, weekly, and twice-a-week periods. You may try to apply a [window function](https://en.wikipedia.org/wiki/Window_function) to limit the effects of considering the signal as a periodic signal of period 8335 days. — francis, Sep 19 '19 at 19:28
Take a look at this and see if it helps, https://stackoverflow.com/questions/52690632/analyzing-seasonality-of-google-trend-time-series-using-fft/52691914 — DrM, Sep 23 '19 at 14:39

How can I convert FFT results for real-world times series analysis?

0 Answers0