具有结构转换的半参数和幂变换门限GARCH建模及其应用

Being affected by the factors of political and economic policies and events, the volatility of the stock market will present regime switching. Thus, it is essential to describe its fluctuations using regime switching model. The existing GARCH family models are established under the condition that the volatility data must meet some certain assumptions, so there are possibilities of model misspecification; while nonparametric GARCH models have the problem of "curse of dimensionality" and are difficult to explain the model estimated. This research explores to establish models that avoid the above defects. We combine the GARCH model with regime-switching to semiparametric GARCH model together, and then establish semiparametric GARCH model with regime-switching, and thus we can establish semiparametric power-transformed and threshold GARCH model with regime-switching. Furthermore, we will study the semi-strong power-transformed and threshold GARCH model and its semiparametric extension. This project will systematically study the stationarity, identiability and estimation methods of those models, and then perform empirical study based on China's Shanghai and Shenzhen stock markets. The parametric part of the established models can provide reasonable explanations for the volatility, and the nonparametric part can reduce the estimation error. These models are the most general volatilities models of financial assets up to now. The theoretical significance of the project is that it establishes theory of semiparametric GARCH family with regime-switching, and it can be applied to risk analysis to China's stock market.

股票市场受到政治经济政策和事件等因素的影响，会导致其波动性出现结构变化，采用结构转换模型描述其波动变化非常必要。现有GARCH模型族是对金融波动数据满足一定条件的假设下建立的，有模型误设的可能；而非参数GARCH模型存在"维数灾难"和模型解释能力有限的问题，本项目建立的模型避免如上缺陷。我们将具有结构转换的GARCH模型与半参数GARCH模型结合起来，建立具有结构转换的半参数GARCH模型，从而建立结构转换的半参数幂变换门限GARCH模型；进一步研究由此发展的半强幂变换门限GARCH及其半参数扩展，系统研究这些模型的平稳性、可识别性，以及估计方法等内容，以我国沪深股市的波动特征进行实证研究。研究建立的模型参数部分对波动性进行合理解释，非参数部分减少估计误差，是国际上最一般的具有结构转换的金融资产波动模型，其意义在于建立具有结构转换的半参数GARCH模型族理论，并应用于我国股市的风险分析。

股票市场受到政治经济政策和事件等因素的影响，会导致其波动性出现结构变化，采用结构转换模型描述其波动变化非常必要。现有GARCH模型族是对金融波动数据满足一定条件的假设下建立的，有模型误设的可能；而非参数GARCH模型存在“维数灾难”和难以解释估计出模型的问题。本项目建立的模型避免如上缺陷。. 我们将具有结构转换的GARCH模型与半参数GARCH模型结合起来，研究建立了具有结构转换的半参数GARCH模型及其实证应用，得到估计结构转换的半参数GARCH模型的迭代算法，并用Matlab程序实现。研究建立了基于结构转换幂变换门限GARCH模型，并对模型进行参数估计和实证分析应用。将上述模型应用于我国沪深股市的波动率建模，然后计算股指波动的在险值VaR和CVaR值。研究利率政策的调整对于不同状态下股市波动性的影响，建立了时变概率结构转换的GARCH/EGARCH模型的估计及其实证分析，并用于分析银行同业拆借利率的变化对于股市波动影响的实证研究。. 研究建立的模型参数部分对波动性进行合理解释，非参数部分减少估计误差，是国际上最一般的具有结构转换的金融资产波动模型，其意义在于建立具有结构转换的半参数GARCH模型族理论，并应用于我国股市的风险分析。