Spurious regression under broken trend stationarity

Abstract

We study the phenomenon of spurious regression between two random variables when the generating mechanism for individual series follows a stationary process around a trend with (possibly) multiple breaks in its level and slope. We develop relevant asymptotic theory and show that spurious regression occurs independently of the structure assumed for the errors. In contrast to previous findings, the spurious relationship is less severe when breaks are present, whether or not the regression model includes a linear trend. Simulations confirm our asymptotic results and reveal that, in finite samples, the spurious regression is sensitive to the presence of a linear trend and to the relative locations of the breaks within the sampleSpurious regression, Structural breaks, Stationarity