I'm having a lil-trouble getting around the definition for a weakly stationary time process from my lectures;
Def. The (auto)covariance function of a time process $X = (X_t)_{t \in \mathbb{Z}}$ is $$\gamma_X(s,t) = \gamma_{s,t} = \mathbb{E}(X_s X_t) - \mu_s \mu_t $$
and
Def. A time series $X = (X_t)_{t \in \mathbb{Z}}$ is weakly stationary if
- $\mu_X(t) = \mu, \forall t\in \mathbb{Z} $
- For every $t,h \in \mathbb{Z}, \gamma_X(t,t+h) =\gamma_X(h)$
The confusion is about $\gamma_X(h)$ since it's only one argument. Does one mean $\gamma_X(h) = \gamma_X(h,h)?$