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I'm newbie to forecast and working on a time series. I begin with splitting data (lets assume there are 100 daily observations) into train set (first 70 days) and test set(last 30 days), then fit Holt Winter and ARIMA model with train set.

Q1: I think the next step is to use trained models to predict day 71-100 and compare with actual data from test set. Which is the correct way to predict day 71-100? (or maybe both are wrong?) A. use trained model + train set to do 30-steps forecast B. use trained model + train set + test set to do 1-step forecast (if this is correct way a code snippet would be very helpful)

Q2: The business goal is to forecast N days, should I take N into consideration during model training/testing/selection process?

Q3: The time series has strong 7-day seasonality, does this effect train/test splitting? i.e, is it preferable to split on full cycle rather than on middle of a cycle?

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Q1-Q2:

Depends on the goal. If you are going to use model to forecast N days ahead then you should test your model by comparing N days ahead forecast and real data from N days ahead. Here is a code psedo code for 1 day ahead testing for a AR model:

https://stats.stackexchange.com/a/503021/293623

You can modify it to N days ahead.

Q3:

It does not affect the model. But it would be better to test on full cycle to understand your results better.

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