The Hallin-Liška Criterion Through the Lens of the Random Matrix Theory

This paper uses large random matrix theory to analyze the workings of Hallin and Liška’s (J Am Stat Assoc 102, 603–617) criterion for determining the number of factors. It focuses on the asymptotic analysis of the Hallin-Liška practical guide for the data-driven choice of the scaling parameter of the penalty function. In a simple static factor framework, we derive the asymptotic representation for the “second stability region,” which determines the parameter choice, and describe asymptotics of the other important features of the Hallin-Liška procedure. We show that, in our simple framework, the Hallin-Liška estimator of the number of factors remains consistent even when the factors are extremely weak.