Consider the stationary ARMA process $(X_t)_t$ with $E(X_t) = 0$ and the covariance function $\gamma(h) = Cov(X_t, X_{t+h})$ (due to stationarity $Cov(X_t, X_{s}) = \gamma(|t - s|)$).

1) What can we say about $(X_t^2)_t$, where the variables are squared?

Is this process also stationary? $E(X_t^2) = \sigma^2\, \forall t$,

but what about $Cov(X_t^2, X_{t+h}^2)$?

2) And can we say anything about $E(X_t\cdot X_s\cdot X_k \cdot X_l)$ for arbitrary $t, s, k, l$?


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