= ARMA(1,1) causal and inverse coefficients
{c}
{title2=$c_j=(\phi+\theta)\phi^{j-1},\quad d_j=-(\phi+\theta)(-\theta)^{j-1}$}
For $|\phi|<1$ and $|\theta|<1$, the <autoregressive moving-average model> $(1-\phi B)X_t=(1+\theta B)\epsilon_t$ has $c_0=d_0=1$ and the displayed coefficients for $j\geq1$. These follow by multiplying the two geometric <power series>. If $\phi+\theta=0$, all later coefficients vanish and the filtered process is <white noise>. Thus root restrictions on an uncancelled nonminimal representation are sufficient but need not be necessary for the process after <common factor cancellation in an ARMA model>.
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