Onatski, A.

Asymptotics of the principal components estimator of large factor models with weakly influential factors

Journal of Econometrics

Vol. 168(2) pp. 244-258 (2012)

Abstract: This paper introduces a drifting-parameter asymptotic framework to derive accurate approximations to the finite sample distribution of the principal components (PC) estimator in situations when the factors’ explanatory power does not strongly dominate the explanatory power of the cross-sectionally and temporally correlated idiosyncratic terms. Under our asymptotics, the PC estimator is inconsistent. We find explicit formulae for the amount of the inconsistency, and propose an estimator of the number of factors for which the PC estimator works reasonably well. For the special case when the idiosyncratic terms are cross-sectionally but not temporally correlated (or vice versa), we show that the coefficients in the OLS regressions of the PC estimates of factors (loadings) on the true factors (true loadings) are asymptotically normal, and find explicit formulae for the corresponding asymptotic covariance matrix. We explain how to estimate the parameters of the derived asymptotic distributi

JEL Codes: C13, C33

Author links: Alexey Onatskiy  

Publisher's Link: http://dx.doi.org/10.1016/j.jeconom.2012.01.034