Lag-two ARCH process
= Lag-two ARCH process
{title2=$X_t=\sqrt{\alpha_0+\alpha_2X_{t-2}^2}\,\varepsilon_t$}
For $\alpha_0>0$ and $0<\alpha_2<1$, the model $X_t=\sqrt{\alpha_0+\alpha_2X_{t-2}^2}\,\varepsilon_t$ splits into independent even-time and odd-time chains in its stationary causal solution. With standard normal noise, $\mathbb EX_t^2=\alpha_0/(1-\alpha_2)$, and its <fourth moment> is finite exactly when $3\alpha_2^2<1$.