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Motivation: I would like to forecast Canadian Inflation Index using N-HITS or N-BEATS model (I have considered both pytorch forecasting package and neuralforecast python packages).

I hope to use exogenous variables such as bank rate, employment rate, labor participation in forecast, and I also want to use the different components of inflation price index (all items, food, goods, services, clothing, energy etc) to improve the model's ability to learn trends and seasonality.

My first attempt: I backshift the exogenous variables and include the same exogenous variables for every time series (i.e.: all-items time series would have same monthly unemployment information as service time series for the same date). I concatenated the different time series into a single long DataFrame. An snip of the test data is below (VALUE is the CPI index for the corresponding category):

Test Data Example

This unfortunate resulted in the N-HITS model creating identical forecasts for every component of inflation (all-items, energy, clothing, etc) - even for components that are drastically different from one another!

- All_items CPI forecast:

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- Foot wear and clothing:

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What is the appropriate way to set up exogenous data for N-HITS when using multiple time series?

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