Modelling Large Dimensional Datasets with Markov Switching Factor Models

TL;DR

This paper introduces a new large-dimensional factor model with regime changes driven by a Markov process, using PCA and EM algorithms for estimation, applicable to financial and macroeconomic datasets.

Contribution

It develops a novel factor model with regime-switching loadings, providing closed-form estimators that do not require knowing the true number of factors.

Findings

Estimates show good finite sample performance in simulations.

Model effectively captures regime changes in large datasets.

Applications demonstrate practical usefulness in finance and macroeconomics.

Abstract

We study a novel large dimensional approximate factor model with regime changes in the loadings driven by a latent first order Markov process. By exploiting the equivalent linear representation of the model, we first recover the latent factors by means of Principal Component Analysis. We then cast the model in state-space form, and we estimate loadings and transition probabilities through an EM algorithm based on a modified version of the Baum-Lindgren-Hamilton-Kim filter and smoother that makes use of the factors previously estimated. Our approach is appealing as it provides closed form expressions for all estimators. More importantly, it does not require knowledge of the true number of factors. We derive the theoretical properties of the proposed estimation procedure, and we show their good finite sample performance through a comprehensive set of Monte Carlo experiments. The empirical usefulness of our approach is illustrated through three applications to large U.S. datasets of stock returns, macroeconomic variables, and inflation indexes.