A note on spurious regressions between stationary series

Abstract

This article examines if the convergent t-test suggested by Sun (2004) is able to solve spurious regressions with stationary series. In brief, we find that the convergent t-test does provide better control over size compared to the usual t-test and its Newey–West modification and, in most cases implementing a pre-whitening procedure size is further controlled.

Notes

¹ Recently, Kiefer and Vogelsang (2005) suggested using M = bT, where b ∊ (0,1) is a fixed number. An obvious trade-off has been found: a small bandwidth (small b) leads to tests with higher power but greater size distortions and a large bandwidth (large b) leads to tests with lower power but less size distortions. Since controlling for size distortions is our main concern, we stick to the choice of ‘M = T’ (i.e. b = 1).