= Autocovariance tail recurrence of a causal ARMA process
{title2=$\gamma_k-\sum_{j=1}^p\phi_j\gamma_{k-j}=0\quad(k>q)$}
For a causal <autoregressive moving-average model> driven by <independent> <white noise>, multiply its recursion by $X_{t-k}$ and take <covariance>. When $k>q$, all driving <white noise> values in its moving-average term occur strictly after $t-k$, so their <covariances> with $X_{t-k}$ vanish. The resulting homogeneous tail recurrence has the same characteristic roots as the <autoregressive model> recursion. Distinct roots of modulus below one give exponential <autocovariance> decay.
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