A Complete Introduction To Time Series Analysis (with R):: Stationary processesII

White Noise data: we can see that it has mean zero and constant variance.

In the last article, we discussed the concepts of weak and strong stationarity, along with the autocovariance function and autocorrelation function (ACF). However, we haven’t seen what these are supposed to be or look like. In this section, we will see some examples along with cool visualizations using R. Let’s get started!

Characterization of stationary processes

We would like to:

1. Show that the mean of the process is independent of t
2. Find some meaningful form for the covariance function, also independent of t

If any of these conditions were to fail (or if the second moments are not finite), our series would become non-stationary. Let’s see some examples, but before, recall a useful identity when working with covariances:

IID Noise