Weak stationarity, or covariance stationarity, is the property of a stochastic process 
with finite second moments that its population
mean is constant and its covariance depends only
on the lag between observations. There are functions 
and 
such that
![E[X_t]=mu](/images/equations/WeakStationarity/NumberedEquation1.svg) |
and
 |
where ![E[Y]](/images/equations/WeakStationarity/Inline4.svg)
denotes the expectation value of 
. These relations hold for all 
and 
.
Weak stationarity does not in general imply strict stationarity. Conversely, strict stationarity implies weak stationarity when the necessary second moments exist.
