基于长记忆和结构突变波动率建模的计量理论与应用研究

本课题在非线性、非平稳时间序列视角下，研究金融资产波动率模型。从计量理论到实证分析，本课题具体解决以下几点问题：（1）长记忆与带有结构突变的时间序列模型拥有不同的概率结构性质，基于这些理论性质差异，我们提出一类判别检验来区分平稳长记忆波动率和带结构变点的非平稳短记忆波动率，推导检验量的大样本性质，从计量理论上掌握波动率的实际产生机制和真实动态结构；（2）我们提出一类自适应的非平稳长记忆波动率模型，在此类模型下讨论模型估计、模型设定检验及拟合优度检验等统计推断问题，且用蒙特卡洛模拟考察小样本表现绩效；（3）对带有结构突变的长记忆波动率模型进行实时预测，解决最优预测带宽选择和最优加权系数赋值等问题；（4）将本课题所建立的一类新的非平稳长记忆波动率模型用于对我国股票市场、汇率市场、期货市场等金融资产波动率的实证分析，计算风险在值、期望损失等风险指标，为防范金融风险提供更可靠的量化工具。

We study financial volatilities in the framework of nonlinear and non-stationary time series. From the econometric theory to the empirical analysis, we mainly focus on the following issues: (1) Based on the distinctly different probabilistic structures between the stationary long memory volatility process and short memory volatility with structural breaks, we propose hypothesis testing to discriminating them. We derive the large-sample properties of the test statistics and understand the true generating mechanism and dynamics of volatility process; (2) We propose a new class of adaptive non-stationary and long memory volatility models. In contrast to the classical volatility models, the new models capture simultaneously both the desirable stylized facts of financial volatilities. We investigate statistical inference under the new models, including model estimation, model specification testing and model diagnostic checking. The finite-sample performance will be demonstrated by Monte Carlo simulations; (3) Investigate forecasting issue of the long memory volatility models with on-going structural changes. Offer the solutions of optimal forecasting windows and optimal down-weighting coefficients in order to obtain the minimum prediction errors; (4) The new theory and methodology proposed here are applied to empirical analysis on financial market in China, such as stock market, exchange rate, future market and calculate the risk indexes, such as VaR, ES. This project can provide new measurement tools for financial risk management and derivative pricing.