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I am taking time-series econometrics this semester and got stuck with the following. Assuming we have $ARMA(1,1)$ model: $Y_t = 0.2Y_{t-1} + ε_t + 0.1ε_{t-1}$ with the estimated variance of $1$.

Another model we have is an $AR(2)$ model using the same data: $Y_t = 0.32Y_ {t-1} - 0.03Y_{t-2} + η_t$ with the estimated variance close to 1. If we forecast $Y_t$ into $h$ periods ahead (with $ε$ and $η$ being white noise), we get the same point forecasts that are similar. Why is it the case that we get the same results?

Would appreciate if you could give a more detailed answer. Thanks

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  • $\begingroup$ Hi! Welcome to our community! I've taken the liberty to edit your question so it's more readalbe for people trying to respond. $\endgroup$
    – David
    May 11, 2021 at 8:42
  • $\begingroup$ Thanks a lot for editing! $\endgroup$
    – user321152
    May 11, 2021 at 8:50

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Predictions of stationary ARMA models will quickly converge towards the mean of the series (treat the AR model as a particular case of an ARMA). Depending on how big $h$ is in your specific case, you may just see that both models are predicting the mean of the series.

Anyway if the models are reasonably good, it should be expected that they output similar predictions even for $h=1$.

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