GARCH(1,1)模型的稳健估计比较及应用

首先阐述了GARCH(1,1)模型稳健估计的构造方法,然后在模型有无异常值扩散效应约束和异常值比例不同的情况下,比较了传统QMLE估计和多种稳健M估计的表现,结果表明:在数据无异常值下,QMLE估计较优;随着异常值比例增加,稳健Andrew估计表现更好;模型施加异常值扩散效应约束对估计有一定改善但不显著.最后选取波动程度不同的两个阶段沪深300指数的收益率,用模型拟合进行了实例比较,在波动程度较大时,Andrew估计效果较优,在波动相对平稳时,LAD估计较优.     

Conditional VaR estimation using Pearson’s type IV distribution

This paper presents a new value at risk (VaR) estimation model for equity returns time series and tests it extensively on Stock Indices of 14 countries. Two most important stylized facts of such series are volatility clustering, and non-normality as a result of fat tails of the return distribution. While volatility clustering has been extensively studied using the GARCH model and its various extensions, the phenomenon of non-normality has not been comprehensively explored, at least in the context of VaR estimation. A combination of extreme value theory (EVT) and GARCH has been explored to analyze financial data showing non-normal behavior. This paper proposes a combination of the Pearson’s Type IV distribution and the GARCH (1, 1) approach to furnish a new method with superior predictive abilities. The approach is back tested for the entire sample as well as for a holdout sample using rolling windows.     

V-uniform ergodicity of a continuous time asymmetric power GARCH(1,1) model

A continuous time asymmetric power GARCH(1,1) model is presented and the V-uniform ergodicity and β-mixing property of the process with exponential decay rate are proved. The V-uniform ergodicity of the COGARCH(1,1) model is obtained as a special case.     

Extreme value distribution of a recursive-type detector in a linear model

We study a CUSUM–type monitoring scheme designed to sequentially detect changes in the regression parameter of an underlying linear model. The test statistic used is based on recursive residuals. Main aim of this paper is to derive the limiting extreme value distribution under the null hypothesis of structural stability. The model assumptions are flexible enough to include rather general classes of error sequences such as augmented GARCH(1,1) processes. The result is underlined by an illustrative simulation study. Research partially supported by NSF grants DMS–0604670 and DMS–065242.     

多维GARCH模型的半参数有效估计

多元GARCH模型的估计一般采用拟极大似然法(quasi maximum likehood),对于这种方法估计的相合性及渐近正态性已经被很多学者证实,然而对于新息列的分布不是多元正态时,这种估计的有效性还没人研究,本文从拟极大似然估计得到的参数相合估计入手,提出用非参数方法估计多元新息列的分布.     

基于动态数据驱动的改进灰色马尔科夫模型黄金价格预测

将黄金数据的尖峰厚尾、异方差性及杠杆效应等统计特征与马尔科夫概率转移矩阵所具有的动态变化规律结合,提出一种改进的灰色马尔科夫模型.模型首先对数据进行统计分析,建立相应的概率统计模型并用此模型对系统发展变化趋势进行拟合.在拟合序列的基础上利用马尔科夫链的动态转移变化建立状态转移概率矩阵,采用动态数据驱动原理对未来每一步数据进行动态预测.模型既是统计方法与数据动态驱动的结合,克服了传统的灰色马尔科夫模型中对数据内在统计规律的忽视,实证表明其预测精度较灰色马尔科夫模型预测高,具有较好的实用性.     

上海证券市场回报率分析——基于ARIMA模型和GARCH模型

本文分析中国上海证券市场回报率。分别通过APdMA模型和GARCH模型,发现若用APdMA模型分析和建立时间序列模型,一次自回归项是不够的,需要高次项,在大多数情形,若运用GARCH模型,则GARCH（1,1）就能够很好的拟合数据。     

多元波动率模型的一些新进展

对多个资产收益率的协方差矩阵建立动态模型是一个非常重要的问题。本文就近些年来该方面研究的一些主要进展进行了综述,特别地介绍了几种基于数据降维技术发展起来的能够适用于高维情形的多元GARCH模型,另外,对于多元波动率的模型诊断与比较方法以及条件协方差矩阵的预测等方面的研究成果也作了分析。     

基于GARCH类模型和SV类模型的沪深两市波动性研究

以CSMAR数据库2007年2月27日至2008年5月14日共297个交易日的上证综指和深证综指的收盘价数据为研究对象,通过比较5类GARCH模型和两类SV模型对上证综指和深证综指样本内(2007年2月27日至2008年2月27日)收益率波动特征的描述能力以及样本外(2008年2月28日至2008年5月14日)收益率波动的预测能力,得出GARCH类模型相比SV类模型更适合描述中国证券市场的波动性.     

Sudden changes in variance and time varying hedge ratios

This paper analyzes the influence of sudden changes in the unconditional volatility on the estimation and forecast of volatility and its impact on futures hedging strategies. We employ several multivariate GARCH models to estimate the optimal hedge ratios for the Spanish stock market including in each one some well-known patterns that may affect volatility forecasts (asymmetry and sudden changes). The main empirical results show that more complex models including sudden changes in volatility outperform the simpler models in hedging effectiveness both with in-sample and out-of-sample analysis. However, the evidence is stronger when the loss distribution tail is used as a measure for the effectiveness (Value at Risk (VaR) and Expected Shortfall (ES)) suggesting that traditional measures based on the variance of the hedged portfolio should be used with caution.