SPURIOUS FACTORS IN DATA WITH LOCAL-TO-UNIT ROOTS

IF 1 4区 经济学 Q3 ECONOMICS Econometric Theory Pub Date : 2024-05-31 DOI:10.1017/s0266466624000094
Alexei Onatski, Chen Wang
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Abstract

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.
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本地到单位根数据中的虚假因素
本文将 Onatski 和 Wang(2021 年,虚假因子分析。Econometrica,89(2),591-614.)扩展到具有异质局部-单位根的高维数据。我们发现了与单位根数据类似的虚假因子现象。也就是说,主成分分析估算出的 "因子 "收敛于不同衰减率的奥恩斯坦-乌伦贝克过程的协方差核的加权平均数的主特征函数。因此,这种 "因子 "反映的是数据的强时间相关性结构,而不是真正的因子通常涉及的任何横截面共性。此外,相对于其他特征值,样本协方差矩阵的主特征值非常大,造成了 "因子 "捕捉了大部分数据共同变化的假象。我们推测,虚假因子现象更普遍地适用于从异质连续时间(或空间)过程的高频采样中获得的数据,并提供了一个例证。
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来源期刊
Econometric Theory
Econometric Theory MATHEMATICS, INTERDISCIPLINARY APPLICATIONS-STATISTICS & PROBABILITY
CiteScore
1.90
自引率
0.00%
发文量
52
审稿时长
>12 weeks
期刊介绍: Since its inception, Econometric Theory has aimed to endow econometrics with an innovative journal dedicated to advance theoretical research in econometrics. It provides a centralized professional outlet for original theoretical contributions in all of the major areas of econometrics, and all fields of research in econometric theory fall within the scope of ET. In addition, ET fosters the multidisciplinary features of econometrics that extend beyond economics. Particularly welcome are articles that promote original econometric research in relation to mathematical finance, stochastic processes, statistics, and probability theory, as well as computationally intensive areas of economics such as modern industrial organization and dynamic macroeconomics.
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