GARCH族模型参数估计的EXCEL实现

一、引言Engle(1982)提出的自回归条件异方差性模型(即ARCH模型),将方差和条件方差区分开来,并让条件方差作为过去误差的函数而变化,从而为解决异方差问题提供了新的途径。由于其对现代金融计量经济学发展的重要影响,Engle也因此项学术成就而获得2003年诺贝尔经济学奖。1986年,Bollerslev在ARCH模型的基础上提出了广义自回归条件异方差(GARCH)模型。此后,许多学者在GARCH(ARCH)模型的结构下,又发展出一系列新的模型,统称为GARCH族模型。     

中国股票市场有效性实证研究

本文使用AR-GARCH-M模型,通过考察股票价格波动是否具有可预测性来检验市场的弱式有效性. 一、模型设定 对市场有效性的早期研究都假设股票收益的方差在不同时期保持不变,但是大量的实证研究表明这一假设不甚合理,不能客观地对金融市场随时间变化的特性进行准确的描述.金融时间序列的一个显著特点是条件异方差性.Engle(1982)提出自回归条件异方差(ARCH)模型,Bollerslev(1986)将其推广到广义ARCH模型(GARCH).这些模型假定收益的误差项服从条件期望为零,条件方差为以前若干期收益误差平方和的条件正态分布,其性质与金融市场的波动聚集性(Cluster)、收益序列的尖峰、厚尾以及非线性等特征相吻合.因此,为了研究中国股票市场的弱式有效性问题,我们用GARCH(1,1)类模型来模拟股市收益率,用模型残差项的条件方差描述股市的波动性.     

基于商业银行汇率风险的经济资本配置

文章首先检验了人民币对美元日汇率收益序列的特征,在此基础上,建立了ARCH、GARCH和EGARCH模型,比较发现GARCH(1,1)模型有最好的拟舍效果.进而利用GARCH(1,1)模型预测条件方差,研究商业银行汇率风险的经济资本配置.     

ARCH族模型在深沪A股中的应用

经典的最小二乘回归假定随机残差序列无自相关,误差的方差为一常数.然而研究金融市场时却发现,大多数时间序列往往具有变方差的特征,即在某些时期的波动十分剧烈,而另一些时期的波动又相对平稳,为了模拟这种波动,提高预测精度,1982年Engle提出了方差随时间变化的自回归条件异方差ARCH模型,Bollerslev又于1986年进一步提出了广义自回归条件异方差GARCH模型,此后,ARCH模型的一些扩展模型也被相继提出,如ARCH-M模型,GARCH-M模型,EGARCH模型等,形成ARCH族模型,并在解释货币和金融时间序列的行为中得到广泛应用.     

STAR模型框架下的wild bootstrap单位根检验

考虑随机误差项存在异方差的情形,文章建立了STAR模型框架下的wild bootstrap单位根检验策略.Monte Carlo模拟研究的结果表明,若时间序列存在GARCH异方差,KSS非线性单位根检验统计量的检验水平扭曲程度要远高于线性ADF统计量,且GARCH特征越明显,扭曲程度越高.无论GARCH特征明显与否,wild bootstrap单位根检验方法都不存在检验水平扭曲,且具有理想的检验势.     

中国股票市场股权溢价的时变性研究

文章使用GARCH、EGARCH和跨期资本资产定价模型(ICAPM)来对1991年1月-2008年6月期间我国股票市场股权溢价的时变性问题进行研究.结果表明,我国股票市场的股权溢价具有明显的随着时间变化的特征,ARCH效应和杠杠效应显著. 模型和模型估计结果表明,我国股票市场的股权溢价并不具有明显的时变性,条件标准差比条件方差的拟合效果要更好一些.     

一类基于非参数回归的条件异方差检验

现有基于参数模型构造的条件异方差检验往往存在模型设定偏误问题。为了避免模型误设对检验结果的影响,并且同时捕获多种条件异方差现象,本文基于非参数回归构造了不依赖于特定模型形式的条件异方差检验统计量。该统计量可视作条件方差和无条件方差之间差异的加权平均,在原假设成立时渐近服从标准正态分布。数值模拟结果一方面表明本文统计量具有良好的有限样本性质,另一方面也说明条件均值模型误设会导致错误地拒绝条件同方差的原假设,凸显了本文引入非参数方法构造条件异方差检验的必要性。实证分析采用本文统计量探讨了国际主要股指收益率的条件异方差现象,得到了与Engle (1982)不同的检验结果,可能意味着股指收益率呈现出非线性动态特征。     

股票市场与黄金市场收益率波动溢出效应研究

文章通过建立GARCH族模型研究股票市场和黄金市场收益的波动性、波动的非对称性以及波动的溢出效应。研究表明:(1)股票市场和黄金市场的收益率均存在显著的ARCH效应;(2)GARCH(1,1)模型能够很好地消除两市收益率的条件异方差性,方差方程中的ARCH项和GARCH项的系数之和接近1,表明冲击对条件方差的影响具有很强的持续性;(3)两市均存在明显的非对称性,所不同的是股票市场中坏消息引起的波动比同等好消息引起的波动要大,而黄金市场中好消息引起的波动比同等坏消息引起的波动要大;(4)股票市场和黄金市场之间存在溢出效应,但是溢出效应是不对称的、单向的。黄金市场的波动能够引起股票市场的波动,而股票市场的波动不能引起黄金市场的波动。     

基于ARCH类模型的中国经济波动性研究

应用ARCH类模型对中国实际GDP的波动率进行了实证研究,利用准极大似然估计方法QML估计三种ARCH类模型(GARCH、T-GARCH和E-GARCH).实证研究表明:GARCH(1,1)模型是最优的拟合模型.这意味着中国经济波动率是变化的,而且GDP实际增长率是对称的.因此,在经济系统自身还不具备自我稳定功能的条件下,外部干预是保证经济平稳过渡的重要条件.     

FIGARCH模型的参数检验与估计

FIGARCH模型是Baillie、Boller-slve、Mikklson在Engle的ARCH模型(1982年)的基础上于1996年提出来的.该模型擅长于反映金融资产的异方差特性以及长记忆的变动特性,它的主要应用领域是金融资产,包括证券、期权、利率等方面.从提出至今,它已被许多人成功地应用到证券市场及汇率市场.     

A Locally Most Mean Powerful Based Score Test for ARCH and GARCH Regression Disturbances

This article considers the twin problems of testing for autoregressive conditional heteroscedasticity (ARCH) and generalized ARCH disturbances in the linear regression model. A feature of these testing problems, ignored by the standard Lagrange multiplier test, is that they are onesided in nature. A test that exploits this one-sided aspect is constructed based on the sum of the scores. The small-sample-size and power properties of two versions of this test under both normal and leptokurtic disturbances are investigated via a Monte Carlo experiment. The results indicate that both versions of the new test typically have superior power to two versions of the Lagrange multiplier test and possibly also more accurate asymptotic critical values.     

Modelling the persistence of conditional variances

This paper will discuss the current research in building models of conditional variances using the Autoregressive Conditional Heteroskedastic (ARCH) and Generalized ARCH (GARCH) formulations. The discussion will be motivated by a simple asset pricing theory which is particularly appropriate for examining futures contracts with risk averse agents. A new class of models defined to be integrated in variance is then introduced. This new class of models includes the variance analogue of a unit root in the mean as a special case. The models are argued to be both theoretically important for the asset pricing models and empirically relevant. The conditional density is then generalized from a normal to a Student-t with unknown degrees of freedom. By estimating the degrees of freedom, implications about the conditional kurtosis of these models and time aggregated models can be drawn. A further generalization allows the conditional variance to be a non-linear function of the squared innovations. Throughout empirical e imates of the logarithm of the exchange rate between the U.S. dollar and the Swiss franc are presented to illustrate the models.     

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, 'Ne apply Davies' approach, and investigate its finite sample performance through a Monte Carlo study.     

Semiparametric ARCH Models

This article introduces a semiparametric autoregressive conditional heteroscedasticity (ARCH) model that has conditional first and second moments given by autoregressive moving average and ARCH parametric formulations but a conditional density that is assumed only to be sufficiently smooth to be approximated by a nonparametric density estimator. For several particular conditional densities, the relative efficiency of the quasi-maximum likelihood estimator is compared with maximum likelihood under correct specification. These potential efficiency gains for a fully adaptive procedure are compared in a Monte Carlo experiment with the observed gains from using the proposed semiparametric procedure, and it is found that the estimator captures a substantial proportion of the potential. The estimator is applied to daily stock returns from small firms that are found to exhibit conditional skewness and kurtosis and to the British pound to dollar exchange rate.     

A test for the presence of conditional heteroskedasticity within arch-m framework

This paper is concerned with testing the presence of ARCH within the ARCH-M model as the alternative hypothesis. Standard testing procedures are inapplicable since a nuisance parameter is unidentified under the null hypothesis. Nonetheless, the diagnostic tests for the presence of the conditional variance is very important since any misspecification in the conditional variance equation leads to inconsistent estimates of the conditional mean parameters. BTo resolve the problem of unidentified nuisance parameter, ‘Ne apply Davies’ approach, and investigate its finite sample performance through a Monte Carlo study.     

Interaction Between Autocorrelation and Conditional Heteroscedasticity: A Random-Coefficient Approach

In applied econometrics, we tend to tackle specification problems one at a time rather than considering them jointly. This has serious consequences for statistical inference. One example of this is considering autocorrelation and autoregressive conditional heteroscedasticity (ARCH) separately. In this article we consider a linear regression model with random coefficient autoregressive disturbances that provides a convenient framework to analyze autocorrelation and ARCH simultaneously. Our stationarity conditions and testing results reveal the strong interaction between ARCH and autocorrelation. An empirical example of testing the unbiasedness of experts' expectations of inflation demonstrates that neglecting conditional heteroscedasticity or misspecifying the autocorrelation structure might result in unreliable inference.     

Estimating high-frequency foreign exchange rate volatility with nonparametric ARCH models

High-frequency foreign exchange rate (HFFX) series are analyzed on an operational time scale using models of the ARCH class. Comparison of the estimated conditional variances focuses on the asymmetry and persistence issue. Estimation results for parametric models confirm standard results for HFFX series, namely high persistence and no significance of the asymmetry coefficient in an EGARCH model. To find out whether these results are robust against alternative specifications, nonparametric models are estimated. Local linear estimation techniques are applied to a nonparametric ARCH model of order one (CHARN). The results show significant asymmetry of the volatility function. To allow for both flexibility and persistence, a higher-order multiplicative model is fitted. The results show important asymmetries in volatility. In contrast to the EGARCH specification, the news impact curves have different shapes for different lags and tend to increase slower at the boundaries.     

Periodic Autoregressive Conditional Heteroscedasticity

Most high-frequency asset returns exhibit seasonal volatility patterns. This article proposes a new class of models featuring periodicity in conditional heteroscedasticity explicitly designed to capture the repetitive seasonal time variation in the second-order moments. This new class of periodic autoregressive conditional heteroscedasticity, or P-ARCH, models is directly related to the class of periodic autoregressive moving average (ARMA) models for the mean. The implicit relation between periodic generalized ARCH (P-GARCH) structures and time-invariant seasonal weak GARCH processes documents how neglected autoregressive conditional heteroscedastic periodicity may give rise to a loss in forecast efficiency. The importance and magnitude of this informational loss are quantified for a variety of loss functions through the use of Monte Carlo simulation methods. Two empirical examples with daily bilateral Deutschemark/British pound and intraday Deutschemark/U.S. dollar spot exchange rates highlight the practical relevance of the new P-GARCH class of models. Extensions to discrete-time periodic representations of stochastic volatility models subject to time deformation are briefly discussed.     

Preliminary test of fit in a general class of conditionally heteroscedastic nonlinear time series

This article is concerned with a general class of conditionally heteroscedastic time series including possibly nonlinear and asymmetric autoregressive conditional heteroscedastic (ARCH) and generalized ARCH models. A problem of preliminary test of fit (PTF, hereafter) within the broad class under consideration is discussed. It is noted that contrary to usual tests in the literature of conditionally heteroscedastic time series, PTF does not require any specification of the conditional variance in advance. Based on the joint limit distributions of sample autocorrelations, a certain Portmanteau-type statistic for PTF is proposed, and its limit is shown to be a chi-square distribution. In addition, some simulation studies, under various innovations, are reported to support our theoretical results.     

An efficiency Bayesian unit root test in Unobserved-ARCH models

This paper investigates the new prior distribution on the Unobserved-Autoregressive Conditional Heteroscedasticity (ARCH) unit root test. Monte Carlo simulations show that the sample size is seriously effective in efficiency of Bayesian test. To improve the performance of Bayesian test for unit root, we propose a new Bayesian test that is robust in the presence of stationary and nonstationary Unobserved-ARCH. The finite sample property of the proposed test statistic is evaluated using Monte Carlo studies. Applying the developed method, we test the policy of daily exchange rate of the German Marc with respect to the Greek Drachma.