{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,1,9]],"date-time":"2026-01-09T17:47:00Z","timestamp":1767980820041,"version":"3.49.0"},"reference-count":28,"publisher":"Cambridge University Press (CUP)","issue":"4","license":[{"start":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T00:00:00Z","timestamp":1717113600000},"content-version":"unspecified","delay-in-days":0,"URL":"https:\/\/www.cambridge.org\/core\/terms"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Econom. Theory"],"published-print":{"date-parts":[[2025,8]]},"abstract":"<jats:p>This paper extends the spurious factor analysis of Onatski and Wang (2021, Spurious factor analysis. <jats:italic>Econometrica<\/jats:italic>, 89(2), 591\u2013614.) 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 \u201cfactors\u201d estimated by the principal components analysis converge to principal eigenfunctions of a weighted average of the covariance kernels of the demeaned Ornstein\u2013Uhlenbeck processes with different decay rates. Thus, such \u201cfactors\u201d 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 \u201cfactors\u201dcapturing much of the data\u2019s 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.<\/jats:p>","DOI":"10.1017\/s0266466624000094","type":"journal-article","created":{"date-parts":[[2024,5,31]],"date-time":"2024-05-31T06:12:06Z","timestamp":1717135926000},"page":"779-816","source":"Crossref","is-referenced-by-count":1,"title":["SPURIOUS FACTORS IN DATA WITH LOCAL-TO-UNIT ROOTS"],"prefix":"10.1017","volume":"41","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-8299-1113","authenticated-orcid":false,"given":"Alexei","family":"Onatski","sequence":"first","affiliation":[{"name":"University of Cambridge"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8701-7467","authenticated-orcid":false,"given":"Chen","family":"Wang","sequence":"additional","affiliation":[{"name":"University of Hong Kong"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"56","published-online":{"date-parts":[[2024,5,31]]},"reference":[{"key":"S0266466624000094_r7","unstructured":"Bykhovskaya, A. , & Gorin, V. 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