Spurious Factor Analysis

Abstract

This paper draws parallels between the principal components analysis of factorless high‐dimensional nonstationary data and the classical spurious regression. We show that a few of the principal components of such data absorb nearly all the data variation. The corresponding scree plot suggests that the data contain a few factors, which is corroborated by the standard panel information criteria. Furthermore, the Dickey–Fuller tests of the unit root hypothesis applied to the estimated “idiosyncratic terms” often reject, creating an impression that a few factors are responsible for most of the nonstationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences.

Estimation of Impulse-Response Functions with Dynamic Factor Models: A New Parametrization

“…There is, however, one major difference between the data used in this paper and those in FG, which concerns variable transformations aimed at making them stationary. As observed by Uhlig (2009) in his discussion of Boivin et al (2008) and recently formalized by Onatski and Wang (2021), estimation of DFMs using non-stationary or highly persistent data may lead to spurious results concerning the factor structure, where a few factors explain a large proportion of the variance in the data. In particular, Onatski and Wang (2021) observed that the first three principal components explain asymptotically over 80 percent of the variation of factorless nonstationary data.…”

“…As observed by Uhlig (2009) in his discussion of Boivin et al (2008) and recently formalized by Onatski and Wang (2021), estimation of DFMs using non-stationary or highly persistent data may lead to spurious results concerning the factor structure, where a few factors explain a large proportion of the variance in the data. In particular, Onatski and Wang (2021) observed that the first three principal components explain asymptotically over 80 percent of the variation of factorless nonstationary data. Thus, persistent variables create factor structure such that autocorrelations are interpreted as comovements between the variables, while the factor sturcture is non-existent when the variables are transformed stationary.…”

On the Factor Structure of Bond Returns

“…It is well known that yields are highly persistent in the time-series dimension with near-unit root behavior. As demonstrated by Uhlig (2009) and Onatski and Wang (2021), principal component analysis of highly-persistent data may produce misleading results. For example, factorless, nonstationary data give rise to a spurious inference of a small number of factors that absorb almost all of the data variation.…”

“…The dominant approach in the term structure literature is to use principal component analysis (PCA) to estimate factors from bond yields. However, working with highly persistent series, such as bond yields, may obscure the true factor structure and produce spurious common variation (Onatski and Wang (2021)). Instead, we follow the seminal work on common factors in the yield curve by Litterman and Scheinkman (1991) and Garbade (1996) that recommends the use of bond returns which are only weakly serially correlated.…”

Quasi Maximum Likelihood Estimation of Non-Stationary Large Approximate Dynamic Factor Models

“…Two comments are worth making. First, it important to stress that initializing the model in first differences (including when determining q and s) is crucial, since it allows us to use PCs without incurring in spurious effects due to the presence of idiosyncratic unit roots (Onatski and Wang, 2019), or linear trends (Ng, 2019).…”