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 ...