Model Selection in Approximate and Dynamic Factor Models

Abstract

The variety in factor modelling for multivariate time series implies the necessity to develop the model selection methodology as the 'optimally' chosen model is not only important for understanding the underlying nature of a certain data generating process, but can also be useful in constructing more efficient forecasts. The majority of the methods developed in the literature on factor models consider their time domain representation, meanwhile the frequency domain representation of factor models for multivariate time series offers a number of attractive Features which can be exploited in developing more efficient estimation and/or model selection methods. The present dissertation presents two novel approaches for model selection for dynamic and/or approximate factor models, DFMs and AFMs, respectively, formulated and estimated in the frequency domain. The first approach combines theoretical findings in simultaneous statistical inference with testing common and idiosyncratic factors for autocorrelation. The second approach is based on the recent theoretical findings in the random matrix theory and presents a cross-validatory method of selecting the a optimala number of common factors.