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Why is forecast error (MAPE) much higher when using weekly periodicity vs monthly? I am using exactly the same data for both.

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Monthly data are more aggregated. The aggregation will compensate for random fluctuations. Therefore monthly data will be much smoother. (Look at plots of your data and compare how "wiggly" monthly vs. weekly data are.) Therefore monthly data are much easier to forecast than weekly (or worse, daily) data.

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