Stationarity

In this section, we provide an overview of stationary and non-stationary time series. Broadly speaking, the main difference between these two types of time series is the statistical properties such as mean, variance, and autocorrelation. They do not vary across time in stationary time series but do change through time in non-stationary time series. Particularly, time series with a trend or seasonality is non-stationary because the trend or seasonality will affect the statistical properties. The following examples illustrate the behaviors of stationary versus non-stationary time series [1]:

Figure 10.12 – Examples of stationary and non-stationary time series

In order to check the stationary properties, we will check the three following conditions:

• The mean is independent of time:

E[X t] = μ for all t

• The variance is independent of time:

Var[X t] = σ 2 for all t

• No autocorrelation...