The Estimation of Time Varying Volatility Based on the Long Stock Return Series with Its Application

The price fluctuations in the stock market and the changes in the rate of return brought by it have attracted the attention of experts. In this context, this paper focuses on the changes in the volatility of long-term asset return series, and being used in analysis of the Shanghai Composite Index. Since the most commonly used GARCH model is available when the observation period is short, and the volatility for long-term asset return series tends to have long memory, this paper proposes an improved time varying GARCH model. In order to fit the change of volatility well, we decompose the variance of volatility into a conditional part and an unconditional part. Through reasonable model transformation, the conditional variance follows the GARCH process, while the unconditional variance, which is changing smoothly over time, is estimated by the nonparametric method (B-spline estimation). The simulation research shows that the model proposed in this paper can better capture the change of volatility in a long run. In order to verify the proposed estimation method, the daily return series of the Shanghai Composite Index are taken for the empirical analysis. In the end, we found that: (i) The nonparametric estimation method proposed in this paper performs well. (ii) The variation of the unconditional variance has a strong correlation with the economic recession; (iii) An apparent variation in the time-varying GARCH model can be explained by the variation of the non-stationary component.