Fast Fourier transformations

Another interesting statistic we often want to compute about time series is the Fourier transformation (FT). Without going into the math, a Fourier transformation will show us the amount of oscillation within a particular frequency in a function.

You can imagine this like the tuner on an old FM radio. As you turn the tuner, you search through different frequencies. Every once in a while, you find a frequency that gives you a clear signal of a particular radio station. A Fourier transformation basically scans through the entire frequency spectrum and records at what frequencies there is a strong signal. In terms of a time series, this is useful when trying to find periodic patterns in the data.

Imagine that we found out that a frequency of one per week gave us a strong pattern. This would mean that knowledge about what the traffic was ton the same day one week ago would help our model.

When both the function and the Fourier transform are discrete, which is the case...