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A non-stationary time series should be not used for regression as it can lead to spurious results. However in case of timeseries without a trend but seasonality, what is the downside of using it in a regression ? The dependent variable is stationary.

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Including a seasonal independent variable represents a problem similar to including one with serial correlation or attempting to fit a misspecified model. Namely, you're attempting to describe a non-linear relationship using a linear model. Using it as is, your estimates are likely to be biased, and your confidence intervals smaller than appropriate.

Assuming you're clear on the seasonality, it's probably preferable to simply deseasonalize the IV in question, else respecify your model.

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