Simultaneous statistical inference in dynamic factor models: Chi-square approximation and model-based bootstrap

Abstract

Statistical inference methodology in dynamic factor models (DFMs) is extended to the multiple testing context based on a central limit theorem for empirical Fourier transforms of multivariate time series. This theoretical result allows for employing a vector of Wald-type test statistics which asymptotically follows a multivariate chi-square distribution under the global null hypothesis when the observation horizon tends to infinity. Multiplicity-adjusted asymptotic multiple test procedures based on Wald statistics are compared with a model-based bootstrap procedure proposed in recent previous work. Monte Carlo simulations demonstrate that both the asymptotic multiple chi-square test with an appropriate multiplicity adjustment and the bootstrap-based multiple test procedure keep the family-wise error rate approximately at the predefined significance level. The estimation algorithm as well as the implementation of the testing procedures are described in detail and a real-life application is performed on European commodity data.