A Simple Test for Spurious Regressions

The literature on spurious regressions has found that the t-statistic for testing the null of no relationship between two independent variables diverges asymptotically under a wide variety of nonstationary data generating processes for the dependent and explanatory variables. This paper introduces a simple method which guarantees convergence of this t-statistic to a pivotal limit distribution, when there are drifts in the integrated processes generating the data, thus allowing asymptotic inference. We show that this method can be used to distinguish a genuine relationship from a spurious one among integrated (I(1) and I(2)) processes. Simulation experiments show that the test has good size and power properties in small samples. We apply the proposed procedure to several pairs of apparently independent integrated variables (including the marriages and mortality data of Yule, 1926), and find that our procedure, in contrast to standard ordinary least squares regression, does not find (spurious) significant relationships between the variables.