Estimation and Inference for High Dimensional Factor Model with Regime Switching

TL;DR

This paper develops a maximum likelihood approach using EM algorithm for high-dimensional factor models with regime switching, enabling consistent detection of regime changes and accurate estimation of factors.

Contribution

It introduces a joint estimation method for high-dimensional factor models with regime switching using EM, with proven consistency and applicability to economic data.

Findings

Method performs well in simulations

Regime switching identified after a single observation

Application detects business cycle turning points

Abstract

This paper proposes maximum (quasi)likelihood estimation for high dimensional factor models with regime switching in the loadings. The model parameters are estimated jointly by the EM (expectation maximization) algorithm, which in the current context only requires iteratively calculating regime probabilities and principal components of the weighted sample covariance matrix. When regime dynamics are taken into account, smoothed regime probabilities are calculated using a recursive algorithm. Consistency, convergence rates and limit distributions of the estimated loadings and the estimated factors are established under weak cross-sectional and temporal dependence as well as heteroscedasticity. It is worth noting that due to high dimension, regime switching can be identified consistently after the switching point with only one observation. Simulation results show good performance of the proposed method. An application to the FRED-MD dataset illustrates the potential of the proposed method for detection of business cycle turning points.