Using fourier analysis for time series prediction

Question

For data that is known to have seasonal, or daily patterns I'd like to use fourier analysis be used to make predictions. After running fft on time series data, I obtain coefficients. How can I use these coefficients for prediction?

I believe FFT assumes all data it receives constitute one period, then, if I simply regenerate data using ifft, I am also regenerating the continuation of my function, so can I use these values for future values?

Simply put: I run fft for t=0,1,2,..10 then using ifft on coef, can I use regenerated time series for t=11,12,..20 ?

Answer 1

I'm aware that this question may be not actual for you anymore, but for others that are looking for answers I wrote a very simple example of fourier extrapolation in Python https://gist.github.com/tartakynov/83f3cd8f44208a1856ce

Before you run the script make sure that you have all dependencies installed (numpy, matplotlib). Feel free to experiment with it. P.S. Locally Stationary Wavelet may be better than fourier extrapolation. LSW is commonly used in predicting time series. The main disadvantage of fourier extrapolation is that it just repeats your series with period N, where N - length of your time series.

Answer 2

It sounds like you want a combination of extrapolation and denoising.

You say you want to repeat the observed data over multiple periods. Well, then just repeat the observed data. No need for Fourier analysis.

But you also want to find "patterns". I assume that means finding the dominant frequency components in the observed data. Then yes, take the Fourier transform, preserve the largest coefficients, and eliminate the rest.

X = scipy.fft(x) Y = scipy.zeros(len(X)) Y[important frequencies] = X[important frequencies] 

As for periodic repetition: Let z = [x, x], i.e., two periods of the signal x. Then Z[2k] = X[k] for all k in {0, 1, ..., N-1}, and zeros otherwise.

Z = scipy.zeros(2*len(X)) Z[::2] = X