Title
Could regressing a stationary series on a non-stationary series obtain meaningful outcomes – A remedy
Authors
Abstract
Our study builds on the foundational work of Granger and Newbold (1974) to address regressing a stationary series, Yt, on a non-stationary series, Xt, (we call it the I0I1 model). Recently, Wong and Yue (2024) conducted simulations and found that the I0I1 model could be spurious. They also show that the statistics Tβ N for testing Hβ 0 : β = β0 versus Hβ; 1 : β ̸= β0 from the traditional regression model (we call it the I0I0 model) cannot be used for the I0I1 model. To bridge the gap in the literature, in this paper, we introduced three remedies to overcome the limitations of the statistics. We conduct simulations and find that our first proposed remedy could correct the spurious problem, but it results in getting a much smaller size, and both our second and third proposed remedies can correct the spurious problem as well as keep the size close to the theoretical benchmark. Thus, we conclude that both Remedies 2 and 3 are good remedies, but not Remedy 1. In addition, we found that the overall average of the rejection rate by using Remedy 2 is 0.0484, while the overall average of the rejection rate by using Remedy 3 is 0.0496, which is closer to the theoretical benchmark. Thus, we conclude that Remedy 3 is the best.
Keywords
Cointegration, stationarity, non-stationarity, regression, time series analysis
How to Cite
Wong, W.-K., Pham, M. T., & Yue, M. (2024). Could regressing a stationary series on a non-stationary series obtain meaningful outcomes – a remedy. The International Journal of Finance, 36, 1–20.