C43. Two stationarity definitions

Topic: Dependence along a series · more questions on this topic
‹ C42 C44 ›

What are strict stationarity and weak stationarity? State the moment conditions in the latter.

Worked answer (click to show)

Definitions/notation. Strict stationarity means every finite-dimensional joint distribution is unchanged by a common time shift. Weak stationarity requires finite second moments, constant \mathbb{E}(X_t)=\mu, and covariance \operatorname{Cov}(X_t,X_{t-k})=\gamma(k) depending only on lag k; neither definition requires independence.