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Could regressing a stationary series on a non-stationary series obtain meaningful outcomes?
Author(s)
Date Issued
2024
Publisher
World Scientific Pub Co Pte Ltd
Journal
ISSN
2010-4952
2010-4960
Citation
Annals of Financial Economics, 2024, vol. 19(3), article no. 2450011.
Type
Peer Reviewed Journal Article
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 [Formula: see text] model). However, very few studies, if there are any, examine the [Formula: see text] 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, [Formula: see text], on a non-stationary time series, [Formula: see text] (that is, [Formula: see text]) 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 [Formula: see text] model and find that the statistics [Formula: see text] for testing [Formula: see text] versus [Formula: see text] from the traditional regression model (we call it [Formula: see text] model) does not have any asymptote distribution with [Formula: see text] and [Formula: see text] as [Formula: see text], and thus, it cannot be used for the [Formula: see text] 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.
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