Strictly Stationary

Definition

A stochastic process $\{Y_t\}$ is strictly stationary

If for any $n\in {\mathbb{Z}}^{+}$, any set of time points $\{t_1,t_2,\dots ,t_n\}$, lag $k$ the joint cumulative distribution function of $(Y_{t_1},Y_{t_2},\dots ,Y_{t_n})$ is identical to that of $(Y_{t_1+k},Y_{t_2+k},\dots ,Y_{t_n+k})$

Relationship with Weak Stationarity

If a stochastic process $\{Y_t\}$ is strictly stationary and $\mathrm{Var}(Y_t)$ is finite for all $t$, then $\{Y_t\}$ is also weakly stationary.