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I have to choose individual GARCH-MIDAS models for some variables. But the BIC value continues to decrease as I increase the lag (its even the case for k=70 and more which is unrealistic) so the BIC, only, isn't really helping.

Is there any condition to choose the maximum lag in GARCH MIDAS? (The significance of some parameter for instance.)

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In my paper Low-frequency Modeling for Capturing Volatility Persistence: A Dynamically Complete Realized EGARCH-MIDAS Model, it was also the case that the log-likelihood was increasing with the allowed number of lags and so will information criteria since the number of parameters are constant.

Our approach was to simply estimate the model for different values of $k$ and stop when the improvement in the log-likelihood was negligible.

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