Covariance Stationary

What is Covariance Stationary?

If we want to estimate future values based on past values, a process like a time series must have specific qualities. It requires that the relationships between its current and previous values stay constant. A time series that is covariance stationary is regarded as such. A time series must exhibit the following three properties:

1. Its mean must be stable over time.
2. Its variance must be finite and stable over time.
3. Its covariance structure must be stable over time

Examples:

If all the terms in a sequence have the same mean, and the covariance between any two terms in the sequence depends only on their relative positions, that is, how far apart they are located from each other, rather than their absolute position, that is, where they are located in the sequence, the sequence is covariance stationary.

Why is It important?

In time series, the idea is significant since correlation coefficients between two series are only meaningful if they are both covariances. Any estimations from the model will have no economic meaning if the series is not covariance stationary.