  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.
