Abstract: This paper studies the periodic transition of the state of China’s stock market and discusses the time-varying distribution characteristics of returns of CSI300 in depth. By introducing the dynamic population reorganization based on the K-means + + clustering algorithm and the chaotic search strategy into the standard particle swarm optimization algorithm, a dynamic multi-population chaotic particle swarm optimization algorithm is proposed, and the initial values of hidden semi-Markov model are further optimized based on this algorithm. The empirical analysis shows that there exist three states in China’s stock market, namely the bear, bull, and volatile markets. A bull market generally follows a bear market, and after a bullish situation, the market has a greater probability of turning to a volatile situation. The volatile state and the bearish state play key roles in the leptokurtic and heavy-tailed characteristics of the stock market, respectively. Based on the decoding results, a mode transformation network is constructed using the coarse-grained method, and key hub modes are identified. Further analysis is conducted on the co-movement of bull and bear states of large-, medium-, and small-cap stocks. There is a significant cyclical polarization between large-cap and medium-or small-cap stocks. Finally, we propose a more accurate out-of-sample forecasting method for the hidden semi-Markov model and prove the practical value of our model via a simple market timing strategy.

Key words: China's stock market, particle swarm optimization, hidden semi-Markov model, out-of-sample forecasting