# ARMA process: squared variables and products of variables

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 $$t, s, k, l$$?