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Think about it this way. If you believe that the data generating process is in fact an ARIMA model, you have a very clear prescription: if you perform both model selection AND estimation anew, basic asymptotics would show that you will reduce your forecasting error. Now, what happens if you aren't crazy and you know the model is false, though potentially ...

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Hi: What you describe is a pretty common problem when estimating time-series models and predicting based off of them. I don't think there's oner answer but rather choices like you mentioned and others. 1) use some fixed rolling window of observations to re-restimate the same model and then predict the next value. 2) use all previous observations + new ...

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Take an ARIMA(1,0,1) for simplicity: \begin{equation} y_t = \phi_0 + \phi_1 y_{t-1} + \theta_1 \epsilon_{t-1} + \epsilon_t. \end{equation} Typically, this is estimated by maximimum likelihood which requires us to make an assumption about the distribution of $\epsilon_t$. Most of the time, people pick a Gaussian distribution and impose homoskedasticity, i....

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