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I'm trying to understand precisely why it is a bad idea to shuffle time-series when splitting train and test data. Like, what is false about shuffling time-series? How does it tamper with the model?

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Because the different observations in a timeseries by definition have an order, i.e. Jan 1st comes before Jan 2nd. If you then shuffle your observations this inherent order will be lost and you might be leaking data, meaning that your model will see data that is actually in the future since Jan 31st might suddenly be before Jan 1st.

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