Covariance stationarity

LEVEL II

An AR model is said to be covariance stationary if:

• is has a finite mean reverting level, which mean that the expected value of the series is constant and finite over time, and
• the volatility is fixed, meaning that the variance is constant and finite over time, and
• the covariance between values at any given lag is constant and finite. 

The requirement for a time series to be covariance stationary is important for autoregressive (AR) models, as these models make the assumption that the data is stationary. If the data is not stationary, then the model will not be accurate.

A series that is not stationary, also known as a non-stationary series, can have a mean and variance that change over time. A non-stationary series can be caused by trend, seasonality, or cyclical patterns in the data. If a series is non-stationary, it cannot be modeled with an AR model without first performing some kind of transformation to make the series stationary such as differentiation or detrending.