The Wold Theorem states that any (weakly) stationary process $(x_t)_{t=-\infty}^{+\infty}$ with zero mean can be decomposed into

$$ x_t=\sum_{j=0}^{\infty} b_j\epsilon_{t-j}\ + \eta_t , $$ where the first summand is the stochastic and the second term a determinstic part.

Let $x_t$ be any (weakly stationary) ARMA(p,q)-process and consider I would like to find the Wold representation of that process. Is it true that the Wold decomposition always coincides with the Moving Avergage MA($\infty$)-representation of that ARMA(p,q)-model, such that $\eta_t=0$ and $b_j$ being the MA weights ?


Yes, conditional on ARMA(p,q) being the true model, what you said is correct.


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