Time series decomposition

The technique of time series decomposition seeks to separate out the components that make up a series, using various techniques. There are several reasons why someone would want to do this, but the three main motivations are usually (a) to independently view the estimated trend component, (b) to provide a series with the seasonal component removed, and (c) to study the dynamics of the seasonal component in isolation.

The school supplies series, for example, was one that we identified as having a roughly level trend and an additive seasonal and error component. We can decompose this series using the function of the same name in R:

> schoolcomps <- decompose(schoolts)
> autoplot(schoolcomps)

The plot of decomposition of an additive time series is as follows:

Figure 11.4: Decomposition of the school supplies series

As you can see, the procedure took its best guesses as to the shapes and levels of its constitute components. In the top panel, we see the actual observed...