= Autocovariance of a causal ARMA(1,1) process
{title2=$\gamma_k=\frac{\sigma^2(\phi+\theta)(1+\phi\theta)}{1-\phi^2}\phi^{k-1}\quad(k\ge1)$}
With positive moving-average sign and $|\phi|<1$, the noise coefficients are $\psi_0=1$ and $\psi_j=(\phi+\theta)\phi^{j-1}$ for $j\ge1$. Summing their overlap gives $\gamma_0=\sigma^2(1+\theta^2+2\phi\theta)/(1-\phi^2)$ and $\gamma_k=\sigma^2(\phi+\theta)(1+\phi\theta)\phi^{k-1}/(1-\phi^2)$ for $k\ge1$. Negative lags follow by symmetry.
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