Decomposing a time series

Seasonal decomposition is the process by which we deconstruct a time series into its components – typically, trend, seasonality, and residuals. The general approach for decomposing a time series is as follows:

1. Detrending: Here, we estimate the trend component (which is the smooth change in the time series) and remove it from the time series, giving us a detrended time series.
2. Deseasonalizing: Here, we estimate the seasonality component from the detrended time series. After removing the seasonal component, what is left is the residual.

Let’s discuss them in detail.

Detrending

Detrending can be done in a few different ways. Two popular ways of doing it are by using moving averages and locally estimated scatterplot smoothing (LOESS) regression.

Moving averages

One of the easiest ways of estimating trends is by using a moving average along the time series. It can be seen as a window that is moved along the time series...