关键词: 混合分布假说, 成交量与波动率关系, 已实现GARCH, 拟极大似然估计, 平稳遍历性

Abstract: We propose a realized Mixture of Distribution Hypothesis model for volume-volatility relation under information asymmetry. The model hypothesizes that the trading volume of the day and the realized measurement provides new information for the second-day potential information flow, which drives informed trading. Sufficient conditions for the stationarity and ergodicity of the time series under our modelling framework are provided. A Gaussian quasi-maximum likelihood estimation method for parameter estimation is proposed and its asymptotic theory is established. Simulation results corroborate our theoretical findings. The proposed model and method are applied to both the U.S. and China stock data. Empirical results show that the increase of trading volume will lead to the increase of the second-day conditional volatility, and that our model fits the data of large-cap, long listed and highly liquid stocks from the Chinese market better than the realized GARCH model as the benchmark volatility model. We find that information trading exists in most stocks. Moreover, our model outperforms widely used existing models in volatility forecasting when applied to Chinese stocks, while the realized GARCH model performs better in U.S. stocks. In summary, our model is more appropriate for describing data of large-cap, long listed and highly liquid stocks from the Chinese market than existing models.

Key words: Mixture of Distribution Hypothesis, Volume-Volatility Relation, Realized GARCH, Quasi-maximum Likelihood Estimation, Stationarity and Ergodicity