A likelihood ratio test for idiosyncratic unit roots in a dynamic-factor model with integrated factors

We consider an exact factor model with the restriction of unobservable common stochastic trends imposed by non-stationary factors as considered by Zhou and Solberger (2012). Conditional on this, we propose a homogenous likelihood ratio test for unit roots in the idiosyncratic components. The likelihood approach has long been overlooked in this framework due to numerical burdens, and though parts of the test are found numerically, the homogeneity restrictions imposed here make the test feasible. In a simulation study, for relatively large T , our test shows better local power than the pooled Fisher-type test of Bai and Ng (2004), while it is roughly equivalent to the LM test of Zhou and Solberger (2012). JEL: C12, C15, C23, C63