Firstly, we employ a three-state hidden semi-Markov model (HSMM) to explain the time-varying distribution of the Chinese stock market returns. Our results indicate that the time-varying distribution depends on the hidden states, represented by three market conditions, namely the bear, sidewalk, and bull markets.
Secondly, we further employ the three-state HSMM to the daily returns of the Chinese stock market and seven developed markets. Through the comparison, three unique characteristics of the Chinese stock market are found, namely “Crazy Bull”, “Frequent and Quick Bear”, and “No Buffer Zone”.
Thirdly, we propose a new diffusion process referred to as the ``camel process'' to model the cumulative return of a financial asset. Its steady state probability density function could be unimodal or bimodal, depending on the sign of the market condition parameter. The overreaction correction is realised through the non-linear drift term.
Lastly, we take the tools in functional data analysis to understand the term structure of Chinese commodity futures and forecast their log returns at both short and long horizons. The FANOVA has been applied to examine the calendar effect of the term structure. An h-step functional autoregressive model is employed to forecast the log return of the term structure
