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I read so many answers in here that I should use IC(information criteria) to determine the optimal lag length in VAR/VECM.
But also it is important to check the residual of VAR/VECM has no-autocorrelation and no-heteroskedasticity.
I use trial and error to find the optimal lag length that makes residual stationary.
So IC is useless to me in some ways.
I wonder I'm doing wrong or not.
I need your advice.

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2 Answers 2

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The choice depends on what you want to do with the model. Different goals justify different selection criteria. Ignoring IC and going for well-behaved residuals may work fine for inference from the model. At the same time, this may be a poor way of finding a model that does well in forecasting (as it will likely be overfitted) or identifying the true data generating process if it happens to be among the candidate models (though this is hardly realistic in practice), and this is where ICs could come in handy.

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  • $\begingroup$ Then if I want to make a model for prediction I can ignore the residual test? I mean, even though the residual is not normal, autocorrelated and heteroskedasticity I can proceed the model and make a prediction? (For simplicity, is it okay to understand that residual test is for inference and IC is for forecasting?) $\endgroup$
    – guest
    Dec 27, 2021 at 12:53
  • $\begingroup$ @guest, it is not that you can ignore these but that if you want to choose a model (among a given set of candidate models) that maximizes the expected likelihood (a measure of forecast accuracy) for a new data point from the same data generating process, then AIC is a principled way of doing so. It does not say how good the set of candidate models is or that there will be no systematic errors, among other things. $\endgroup$ Dec 27, 2021 at 21:26
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Normally, you must run a function like varselect in R, with sqrt(T) max number of lags, and then stick to the BIC (SIC) selected lags. However, if your data is seasonal, you must include at least the number of seasons selected, so as to reduce the correlation of your errors. This should be enough.

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  • $\begingroup$ What objective does this strategy serve? (Why BIC, not another IC? Why make an exception in the seasonal case but not in the nonseasonal case?) (Frankly, I doubt there is a justification that this serves any standard purpose.) $\endgroup$ Dec 27, 2021 at 21:29
  • $\begingroup$ BIC is more conservative than AIC, and tends to select more simple models; furthermore it chooses the true model if provided on the choices. In time series data, BIC works better empirically. The reason to include at least the number of lags of your seasonal data, is because you want to include this information on your model, so excluding the lag of seasonal, would introduce correlation on the errors. $\endgroup$ Dec 27, 2021 at 21:53
  • $\begingroup$ While in some narrower context it might be approximately true, the claim In time series data, BIC works better empirically in its general form is clearly wrong. But more importantly, what objective does this strategy serve? I see a conflict between BIC and inclusion of the seasonal number of lags, as BIC serves one purpose (and is optimal with respect to it, given certain assumptions -- there is a well developed theory for it) while the latter must serve another (I do not know what it is, but it might be possible to define). $\endgroup$ Dec 28, 2021 at 7:05

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