Equivalent sample sizes in time series regressions

Abstract

This article studies confidence intervals for regression parameters in time series settings. An equivalent sample size method is proposed that retains the simple interval structure inherent with white noise model errors, but modifies the sample size to account for the serial autocorrelations present in the errors. This makes the interval perform akin to weighted least squares intervals. The accuracy of the approach is demonstrated in three common regression problems. A noteworthy by-product of the work identifies explicit variances of several classical regression statistics in time series settings.

Keywords:

• ANOVA
• Autocorrelation
• Confidence interval
• Degrees of freedom
• Ordinary least squares
• Regression
• Time series
• Weighted least squares

Acknowledgements

The authors thank National Science Foundation Grant DMS 0304407 for financial support. The referee is thanked for several insightful comments.