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SPURIOUS FACTORS IN DATA WITH LOCAL-TO-UNIT ROOTS

Published online by Cambridge University Press:  31 May 2024

Alexei Onatski Open the ORCID record for Alexei Onatski [Opens in a new window]  and
Chen Wang Open the ORCID record for Chen Wang [Opens in a new window]
Alexei Onatski
Affiliation:
University of Cambridge
Chen Wang*
Affiliation:
University of Hong Kong
*
Address correspondence to Chen Wang, Department of Statistics and Actuarial Science, University of Hong Kong, Pokfulam, Hong Kong, China, [email protected]
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Abstract

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This paper extends the spurious factor analysis of Onatski and Wang (2021, Spurious factor analysis. Econometrica, 89(2), 591–614.) to high-dimensional data with heterogeneous local-to-unit roots. We find a spurious factor phenomenon similar to that observed in the data with unit roots. Namely, the “factors” estimated by the principal components analysis converge to principal eigenfunctions of a weighted average of the covariance kernels of the demeaned Ornstein–Uhlenbeck processes with different decay rates. Thus, such “factors” reflect the structure of the strong temporal correlation of the data and do not correspond to any cross-sectional commonalities, that genuine factors are usually associated with. Furthermore, the principal eigenvalues of the sample covariance matrix are very large relative to the other eigenvalues, creating an illusion of the “factors”capturing much of the data’s common variation. We conjecture that the spurious factor phenomenon holds, more generally, for data obtained from high frequency sampling of heterogeneous continuous time (or spacial) processes, and provide an illustration.

Type
ARTICLES
Information
Econometric Theory , First View , pp. 1 - 38
Copyright
© The Author(s), 2024. Published by Cambridge University Press

Footnotes

The authors would like to thank Peter C.B. Phillips, Yixiao Sun, and three anonymous referees for valuable suggestions that deepen our understanding of the spurious factor phenomenon. Chen Wang’s research is supported by the Research Grants Council of Hong Kong (Grant No. ECS 27308219) and the National Natural Science Foundation of China (Grant No. 72033002).

References

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