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Hi. I've identified this as a AR(1) model as the ACF clearly shows a slow decay and the PACF seems like a cut off after lag 2. However, can it also be a ARMA (1,1) model because PACF seems like a damped sinusoid too?

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I would actually suggest an AR(2) since the PACF cuts off at lag 2. You can also try ARMA(1,1). However, the ACF does not decay that quickly, are you sure that your data is stationary? If you can add a plot of your data it will be helpful. You can use the Augmented Dickey-Fuller to test for stationarity. More information on that test here.

Remember to make sure that all the parameters are statistically significant and that the residual series is white noise before you use the model for forecasting.

This post should also be helpful in answering your question.

Hope this helps :)

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