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I have a dataset that contains monthly data for the past four decades. I understand that if I use 5-fold cross validation, I need to randomly pick training set and testing set. Can I use data from the most recent two years as the testing set? If so, how should I revise the procedure? Thanks!

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Yes you can, since standard CV doesn't work for time series data. See: https://www.otexts.org/fpp2/accuracy.html

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