Simultaneous Statistical Inference in Dynamic Factor Models

Based on the theory of multiple statistical hypotheses testing, we elaborate likelihood-based simultaneous statistical inference methods in dynamic factor models (DFMs). To this end, we work up and extend the methodology of Geweke and Singleton (1981) by proving a multivariate central limit theorem for empirical Fourier transforms of the observable time series. In an asymptotic regime with observation horizon tending to infinity, we employ structural properties of multivariate chi-square distributions in order to construct asymptotic critical regions for a vector of Wald statistics in DFMs, assuming that the model is identified and model restrictions are testable. A model-based bootstrap procedure is proposed for approximating the joint distribution of such a vector for finite sample sizes. Examples of important multiple test problems in DFMs demonstrate the relevance of the proposed methods for practical applications.