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To identify the best lags , try to fit models with different lag choices.Plotting of ACF and PACF could give a sense of different lags choices. Further to this BIC could be used to determine for which AR and MA lag BIC is getting minimised.


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Generally it depends on the model you need to compare; anyway, if I understood your question, you have to estimate the model (2) and in this case it is convenient to compare the Bayesian Information Criterion only for the model (2), since it is exactly what you want to run in the end. Said that, I suggest you to look at the different criteria that exists in ...


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Something I do to find new ideas is read papers in Google Academic related to the topic. Find papers under "quantitative strategy", "trading strategy", etc and you will find interesting things. My experience is that they don't tend to work, but they provide with ideas that you can mix and maybe find something by yourself.



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