I have read that using R-squared for time series is not appropriate because in a time series work, R-squared is no longer unique. Why is this?
Hi! You asked a good question. Btw, where did you read that?
R2 is an in-sample metric. If you try to compare alternative time-series models using R2, this can lead to wrong conclusions: R2 maybe high due to over-fitting.
Let me recommend our chapter addressing the issue of choosing a good error metric for time series models:
Chapter Forecast Error Measures: Critical Review and Practical Recommendations
Generally, in case of one series we recommend out-of-sample MAE, for comparisons across many series we propose the AvgRelMAE scheme.
R square should not be the only diagnostics / evaluation tool.
R square may be a biased estimate. Adjusted R square may be better. R square may be high if you are over fitting the model.
I tried to look this up, but I did not find anything. Typically I do not place much value in R-squared (or Adjusted R-Squared) when I evaluate my models, but a lot of my colleagues (i.e. Business Majors) are absolutely in love with R-Squared and I want to be able to explain to them why R-Squared in not appropriate in the context of time series.
This link me ay benefit you: https://statisticsbyjim.com/regression/r-squared-too-high/
For time series, Stationary R-squared is preferable to ordinary R-squared when there are trends or seasonal patterns. In order to select the best fit model, the model with the lowest MAE or RMSE value should be selected.
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