Handling Seasonality in Regression Predictors

Summary

The document asks whether a seasonal but trendless independent variable can be used in a regression when the dependent variable is stationary. The answer cautions that seasonality in a predictor can create problems similar to serial correlation or model misspecification. A linear specification may fail to capture the variable’s nonlinear seasonal relationship, potentially biasing estimates and making confidence intervals too narrow.

The suggested remedies are to remove the known seasonal pattern from the predictor or to respecify the model to represent it appropriately. The answer is conceptual and gives no data, diagnostic procedure, or empirical comparison. It also does not specify how seasonality should be estimated, or address possible interactions with the dependent variable. The central lesson is to model seasonal structure rather than assume that a stationary dependent variable alone makes the regression reliable.

Key ideas

• A seasonal predictor can create specification problems even when it has no trend.
• A linear model that ignores seasonal structure may produce biased estimates and overconfident intervals.
• Deseasonalizing the predictor or revising the model specification are proposed remedies.
• The document provides no empirical test or detailed seasonal adjustment procedure.

Tags

# Seasonality in Independent Variable in Regression


# Seasonality in Independent Variable in Regression












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.

## Answer by Chris (score 1)

https://quant.stackexchange.com/a/49939

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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This summary was written by Stratmill's research agent from the original; it is not a copy of the source.