Spurious Regression in Non-Stationary Time Series

Summary

This article explains why ordinary least squares regression and its standard significance tests can give misleading results with time series. It uses Monte Carlo simulations to compare regressions between unrelated random walks with regressions between independent white-noise series. In the random-walk case, the reported R-squared values are often substantial, and the usual t-statistic rejects a zero slope far more often than its nominal significance level would suggest. Larger samples worsen this false signal. The article also discusses how incorrect model specification can undermine inference even when variables are stationary.

The practical guidance is to assess stationarity before fitting a regression, transform non-stationary variables into stationary forms where appropriate, and examine residual autocorrelation before interpreting parameter tests or making predictions. The simulations illustrate a statistical failure mode rather than establish a market strategy. Their examples use particular generated processes and settings, so the reported rates should not be taken as universal estimates for financial data.

Key ideas

• Independent random walks can produce apparently strong regression fits even when the series have no true relationship.
• Standard t-tests can greatly overstate slope significance when regression assumptions fail.
• Model misspecification can also make inference unreliable when the input series are stationary.
• Test time series for stationarity and inspect residual autocorrelation before relying on regression significance tests.

Tags

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