A Complete Introduction To Time Series Analysis (with R):: Stationary processes
In the last article, we discussed two important models with structure: the trend decomposition model and seasonal variation. We said that one of the most important steps in the general strategy for time series analysis was to remove the signal, i.e., remove either the estimated trend or seasonality or both. In this section, we will talk about stationary processes, and what it means to be stationary. Let’s dive right into it!
Stationary Processes
Let’s consider some time-series process Xt. Informally, it is said to be stationary if, after certain lags, it roughly behaves the same. For example, in the graph at the beginning of the article, we see that although there is some fluctuation, the points seem to wander around zero, in particular, this is called a mean-zero process. We will define more precisely what this means next. For this purpose, we will focus on studying the second moments, i.e., mean, covariance, and variance of a certain process.
There are two kinds of stationarity: weak stationarity and strong stationarity. Both of these are defined below. If you need a refresher…
