Could regressing a stationary series on a non-stationary series obtain meaningful outcomes?

Wing-Keung Wong and Mu Yue
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Wing-Keung Wong: Department of Finance, Fintech Center, and Big Data Research Center, Asia University; Department of Medical Research, China Medical University Hospital, Taiwan; Business, Economic and Public Policy Research Centre, Hong Kong Shue Yan University; The Economic Growth Centre, Nanyang Technological University
Mu Yue: Engineering Systems and Design, Singapore University of Technology & Design

No 2504, Economic Growth Centre Working Paper Series from Nanyang Technological University, School of Social Sciences, Economic Growth Centre

Abstract: We have read many papers in the literature and found that some papers report results of regressing a stationary time series on a non-stationary time series (we call it the IOI1 model). However, very few studies, if there are any, examine the IOI1 model and the robustness of inference in such settings remains an open question. To bridge the gap in the literature, in this paper, we investigate whether regressing a stationary time series, Yt, on a non-stationary time series, Xt (that is, Yt = α+βXt +ut) could get any meaningful result. To do so, we first conduct a simulation and find regressing a stationary time series on a non-stationary time series could be spurious. Thereafter, we develop the estimation and testing theory for the I0I1 model and find that the statistics Tβ N for testing Hβ 0 : β = β0 versus Hβ 1 : β ̸= β0 from the traditional regression model (we call it IOI0 model) does not have any asymptote distribution with E(Tβ N) → ∞ and V ar(Tβ N) → ∞ as N → ∞, and thus, it cannot be used for the I0I1 model. We have found other interesting results as shown in our paper. Thus, our paper extends the spurious regression literature to cover a previously unexplored case, thereby contributing to a more comprehensive understanding of time series modeling and inference.

Keywords: Cointegration; stationarity; non-stationarity. (search for similar items in EconPapers)
Pages: 28 pages
Date: 2025-04
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