How signal processing can be used to identify patterns in complex time series

The trend and seasonality can be accounted for in a linear model by including sinusoidal components with a given frequency. However, finding the appropriate frequency for each sinusoidal component requires a little more digging. This post shows how to use fast Fourier transforms to find these frequencies. For the purposes of this post, we will only focus on the T(t) and S(t) components. The actual model fitting will be done in a separate post.