Onatski, A. and Wang, C.

Spurious Factor Analysis

CWPE2003

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 collaborated 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 non-stationarity in the data. We warn empirical researchers of these peculiar effects and suggest to always compare the analysis in levels with that in differences.

Keywords: Spurious regression, principal components, factor models, Karhunen-Loève expansion.

Author links: Alexey Onatskiy

PDF: https://www.econ.cam.ac.uk/research-files/repec/cam/pdf/cwpe2003.pdf