Using Hidden Markov Switching-Mixed Normal Distribution Model to Study the Distribution of Chinese Stock Index Returns

Understanding the distribution of financial asset returns is critical for investment and risk management. The traditional assumption of normal distribution does not well describe the skewness and kurtosis of log returns. Most of the currently proposed return distribution models lack the capability to allow time-varying distribution. Thus in this paper, we introduce Markov switching structure into the distribution of Chinese stock index returns, propose the hidden Markov switching-mixed normal distribution(HMS-MND) model, and give the Expectation-Maximization(EM) algorithm for model parameter estimation. The log daily and weekly returns on the major stock indexes of Shanghai stock exchange are used for empirical tests. Parameter estimates as well as likelihood ratio test results show that, the introduction of Markov switching structure could significantly improve the model´s fitting capability. It is also shown that HMS-MND model could well describe the statistics of stock index log returns. Therefore, we argue that using hidden Markov switching-mixed normal distribution model to study the distribution of Chinese stock index returns is of practical value.