Research And Application Of Markov Transition Dynamic Factor Model

The Markov switching dynamic factor model（MS-DFM）is widely used in the measure of the business cycle and identifying the business cycle turning points.In this paper,a new estimation method is proposed for the MS-DFM model,which is denoted as two-step EM method.In the existing two-step estimation method for MSDFM model,the first step is generally directly based on the factor model,where the model parameters and factor scores are estimated by using the principal component method or the maximum likelihood estimation method.While the simulation studies show that the estimates of factor scores behaved poorly due to that the difference of the mean and the variance of the factor under different stats are ignored in the first step.Thus we modified the usual two-step method as follows.In step 1,we fit a mixture factor model by re-parameter the MS-DFM model with the EM algorithm,where both of the factors and states are treated as the latent variables.Then the parameters corresponding the factor models and factor scores can be estimated in Step 1.In the second step,a Markov switching auto regression model（MS-AR）will be fitted based on the estimated factor scores in Step1 by the EM algorithm,where the states are also treated as latent variables here.Then the parameters corresponding the auto regression which are changing with the states and the latent states can be estimated in the second step.Since Step 1 considers the latent group along with the time varying.Its factor score can better reflect the differences in different market states compared with the usual two-step method.Finally,the MS-DFM model is used to measure the stock market cycle and identify the cycle turning points based on the closing pricing of 111 stocks in China’s pharmaceutical industry from 2000.1 to 2022.3.Unlike the usual stock market cycle identification methods,which are usually based on some composite index,this paper assume that the volatility of stock prices are driven by one or several common factors,and the stock market cycle information can be obtained from the latent factors.