= Two-geometric-coefficient expansion of a causal ARMA(2,1) process
{title2=$\psi_j=ar^j+ds^j$}
When the transfer function is $(1+\theta z)/((1-rz)(1-sz))$ with distinct $r,s$ of modulus less than one, partial fractions give coefficients $\psi_j=ar^j+ds^j$, where $a+d=1$ and $-as-dr=\theta$. White-noise orthogonality gives covariance at lag $h\geq0$ as $\sigma^2[a^2r^h/(1-r^2)+d^2s^h/(1-s^2)+ad(r^h+s^h)/(1-rs)]$. This combines stable recursion with a closed geometric-sum covariance.
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