Application of hidden Markov switching moving average model in the stock markets: Theory and empirical evidence

In this paper, we propose a hidden Markov switching moving average model (MS-MA model) to extend the moving average model when the dynamic process of stock returns is predictable. That is, hidden Markov chain can be utilized to better describe the stock return dynamics when moving averages are correlated. Based on the MS-MA model, a recursive method of EM algorithm for parameter estimation is proposed and a numerical analysis is demonstrated. Furthermore, we empirically test the hidden Markov chain model using Dow Jones thirty stocks' data. The empirical results show that the dynamic process of stock returns exhibits MS-MA property, meaning the moving averages of stock returns are correlated. Therefore, the MS-MA model allows us to better understand and to predict stock return stochastic process. This model also helps in pricing equity derivatives.