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I am trying to figure out the best approach for my prediction task. I have a dataset with four variables: year ranging from 2010 to 2022, categorical variables $A$ and $B$, and numeric target variable T. I have numeric data that describes each category in $A$ and $B$, and can be used as embeddings for these instead of the raw categories. Not all categories in $A$ and $B$ occur every year, in fact most combinations occur over only one to two years. The average of my target $T$ seems to show a strong increasing trend. The goal of my problem is to predict target $T$ for future years for a new data sample.

The question is: how can I capture the global trends in $T$ over time while predicting using $A$ and $B$?

Time agnostic models like random forests and boosting would capture the dependencies between $A$,$B$ and $T$ but are not known to capture time trends well. On the other hand, since most $A$x$B$ combinations have data for only one year, I am not sure how I would use time sequence based methods like ARIMA or LSTM.

What approach should I take to my problem? Any help would be greatly appreciated!

PS: My test set may contain unseen categories for A and B, so use of the numeric embeddings is a must.

(Cross posted from stats.stackexchange :) )

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