Spurious Relationships For Nearly Non-stationary Series

Abstract

Literature shows that the regression of independent and (nearly) non-stationary time series could result in spurious outcomes. In this paper, we conjecture that under some situations, the regression of two independent and nearly non-stationary series does not have any spurious problem at all. To check whether our conjecture holds, we set up several situations and conduct simulation to justify our conjecture. Our simulation shows that under some situations, the chance that the regressions being spurious is very high for all the cases simulated in our paper. Nonetheless, under some other situations, our simulation shows that the rejection rates are much smaller than the 5\% level of significance for all the cases simulated in our paper, implying that our conjecture could hold under some situations that regression of two independent and nearly non-stationary series does not have any spurious problem at all.

Keywords: Co-integration, Stationarity, Nearly Non-Stationarity, Spurious Problem, Regression