Determining the number of factors after stationary univariate transformations

Abstract

A very common practice when extracting factors from non-stationary multivariate timeseries is to differentiate each variable in the system. As a consequence, the ratiobetween variances and the dynamic dependence of the common and idiosyncraticdifferentiated components may change with respect to the original components. In thispaper, we analyze the effects of these changes on the finite sample properties of somepopular procedures to determine the number of factors. In particular, we consider theinformation criteria of Bai and Ng (2002), the edge distribution of Onastki (2010) andthe ratios of eigenvalues proposed by Ahn and Horenstein (2013). The performance ofthese procedures when implemented to differentiated variables depend on both theratios between variances and dependences of the differentiated factor and idiosyncraticnoises. Furthermore, we also analyze the role of the number of factors in the originalnon-stationary system as well as of its temporal and cross-sectional dimensions.