Discussion of article "Frequency domain representations of time series: The Power Spectrum"

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New article Frequency domain representations of time series: The Power Spectrum has been published:

In this article we discuss methods related to the analysis of timeseries in the frequency domain. Emphasizing the utility of examining the power spectra of time series when building predictive models. In this article we will discuss some of the useful perspectives to be gained by analyzing time series in the frequency domain using the discrete fourier transform (dft).

Next,we examine the power spectrum of the error distribution. A good prediction model will have residuals that are white noise, which means that the power spectrum of the error distribution should be relatively flat across all frequencies. Prominent peaks in the power spectrum at any frequency suggest that the prediction model is not capturing all of the information in the time series data and further tuning may be necessary. The problem is that in reality the power spectrum of white noise is not usually flat as is expected. Just look at the spectrum of a white noise series generated from the code below.

int num_samples = 500;
   double inputs[];
   MathSrand(2023);
   ArrayResize(inputs,num_samples);
   
   for (int i = 0; i < num_samples; i++) 
    {
        inputs[i] = ((double)rand() / SHORT_MAX) * 32767 - 32767/2;
    }

Author: Francis Dube