A Simple Diagnostic for Time-Series and Panel-Data Regressions

Abstract

We introduce a new regression diagnostic, tailored to time-series and panel-data regressions, which characterizes the sensitivity of the OLS estimate to distinct time-series variation at different frequencies. The diagnostic is built on the novel result that the eigenvectors of a random walk asymptotically orthogonalize a wide variety of time-series processes. Our diagnostic is based on leave-one-out OLS estimation on transformed variables using these eigenvectors. We illustrate how our diagnostic allows applied researchers to scrutinize regression results and probe for underlying fragility of the sample OLS estimate. We demonstrate the utility of our approach using a variety of empirical applications.

Keywords: regression diagnostic, relative contributions of different frequencies, high time-series persistence and spurious regressions, trigonometric basis functions, orthogonalization, leave-one-out frequency approach

JEL Classification: C12, C13, C22, C23