股市波动率的短期预测模型和预测精度评价

基于幂转换以及不设定扰动项的具体相关结构和分布形式,构建了半参数的短期预测模型来预测中国股市的波动率.模型采用基于极值估计量的两阶段估计法进行估计,估计方法的小样本性质表现良好.此外,还通过具有Bootstrap特性的SPA检验实证比较了新模型与其他6种预测模型的预测精度.实证结果表明,在各种损失函数下,半参数短期预测...     

金融市场高维波动率的扩展广义正交GARCH模型与参数估计方法研究

本文对Van der Weide(2002)的广义正交GARCH模型进行扩展,提出反映金融资产收益波动性特征,具有"杠杆效应"的广义正交GARCH模型。由于这种扩展的广义正交GARCH模型在高维数据中面临参数估计困难,本文从交互信息理论视角研究模型的参数估计问题,在理论上证明基于交互信息最小化的多元GARCH模型参数估计与基于极大似然函数参数估计的联系和区别,并在提出的扩展广义正交GARCH模型框架下,采用不同的统计技术实现基于交互信息最小化的参数估计方法,避免了传统极大似然函数估计需要事先正确指定标准化残差概率密度函数和高维运算困难,计算效率较高,使多元GARCH模型在高维数据中可以应用。最后,根据全球主要金融市场的15种股票指数数据,通过实证研究对建立的扩展广义正交GARCH模型及其参数估计方法有效性进行评价与检验。实证研究表明了本文提出的扩展广义正交GARCH模型与参数估计方法的优势。     

Inference in Arch and Garch Models with Heavy–Tailed Errors

ARCH and GARCH models directly address the dependency of conditional second moments, and have proved particularly valuable in modelling processes where a relatively large degree of fluctuation is present. These include financial time series, which can be particularly heavy tailed. However, little is known about properties of ARCH or GARCH models in the heavy–tailed setting, and no methods are available for approximating the distributions of parameter estimators there. In this paper we show that, for heavy–tailed errors, the asymptotic distributions of quasi–maximum likelihood parameter estimators in ARCH and GARCH models are nonnormal, and are particularly difficult to estimate directly using standard parametric methods. Standard bootstrap methods also fail to produce consistent estimators. To overcome these problems we develop percentile–t, subsample bootstrap approximations to estimator distributions. Studentizing is employed to approximate scale, and the subsample bootstrap is used to estimate shape. The good performance of this approach is demonstrated both theoretically and numerically.     

Likelihood‐Based Estimation of Latent Generalized ARCH Structures

GARCH models are commonly used as latent processes in econometrics, financial economics, and macroeconomics. Yet no exact likelihood analysis of these models has been provided so far. In this paper we outline the issues and suggest a Markov chain Monte Carlo algorithm which allows the calculation of a classical estimator via the simulated EM algorithm or a Bayesian solution in O(T) computational operations, where T denotes the sample size. We assess the performance of our proposed algorithm in the context of both artificial examples and an empirical application to 26 UK sectorial stock returns, and compare it to existing approximate solutions.     

多元GARCH 建模及其在中国股市分析中的应用

简要回顾了一元ARCH类模型的发展过程,介绍了多元GARCH类模型的四种形式.针对传统基于梯度信息的多元GARCH模型估计方法的不足,提出了基于遗传算法的似然估计方法,并利用中国股市数据进行了实证研究.结果说明中国股市存在着波动的持续性和显著的二元GARCH效应,并且沪、深股市不存在协同持续性.     

多元GARCH 建模及其在中国股市分析中的应用

简要回顾了一元ARCH 类模型的发展过程,介绍了多元GARCH 类模型的四种形式. 针对 传统基于梯度信息的多元GARCH 模型估计方法的不足,提出了基于遗传算法的似然估计方 法,并利用中国股市数据进行了实证研究. 结果说明中国股市存在着波动的持续性和显著的二 元GARCH 效应,并且沪、深股市不存在协同持续性.     

基于数据驱动平滑检验的密度预测评估方法——以香港恒生指数、上证综指和台湾加权指数为例

本文提出了样本内和样本外密度预测评估的数据驱动平滑检验（data-driven smooth test）方法，并分别采用Newey-Tauchen的方法以及West-McCracken的方法来纠正参数估计对样本内和样本外密度预测评估的影响。运用本文提出的检验方法，我们比较了各种最大熵GARCH模型对中国三个股指数据（香港恒生指数、上证综合指数和台湾加权指数）的样本内和样本外预测绩效。结果显示：（1）最大熵GARCH模型可以用来刻画中国股指数据的典型化事实，GARCH模型中考虑了厚尾和偏态特征的Pearson IV分布对中国股指收益率的样本外预测绩效是很重要的；（2）具有较好样本内拟合优度和样本内预测效果的模型未必有很好的样本外密度预测效果，考虑到样本外预测的重要性，实际应用中我们应采用具有较好样本外预测效果的模型。     

双长记忆GARCH族模型的预测能力比较研究——基于沪深股市数据的实证分析

GARCH族模型在金融风险的度量中有着广泛的应用。在考虑股市收益率和波动率序列双长记忆性的基础上,基于上证综合指数和深圳成份指数的日收盘价序列,从证券投资风险量化的角度,引入受险值VaR和相对正确符号指标PCS作为模型预测误差衡量指标,比较分析了双长记忆GARCH族模型在不同分布假设情况下的的拟合与预测精度。结果显示:偏t分布能较好描述沪深股市的厚尾特征;在较小的VaR水平下ARFIMA(2,d₁,0)-FIAPARCH(1,d₂,1)-skt模型对股市波动风险具有较强的预测能力,而ARFIMA(2,d₁,0)-HYGARCH(1,d₂,1)-skt对股市的涨跌趋势具有较强的预测能力。     

深圳股市时变Beta、条件CAPM实证研究

建立Engle(2002)提出的动态条件相关多元GARCH模型计算深圳股市诸行业指数2001/07/02～2005/07/15期间的时变Beta系数,进而对系统风险Beta系数与收益的关系进行传统的检验和由Pettengill et al.(1995)提出的条件检验,并且探讨了非系统风险、总风险在资产定价中的作用.研究结果表明,Beta与收益间不存在传统的无条件相关关系;部分行业指数的Beta系数与收益符合条件相关关系:当超额市场收益大于0(上市场)时,Beta和收益正相关;当超额市场收益小于0(下市场)时,Beta与收益负相关.但对大多数指数而言,Beta与收益仅在下市场时呈显著的负相关关系.同时非系统风险以及总风险均得到了补偿,表明深圳股市的投资者并没有充分分散化其投资,政府应大力发展机构投资者.     

Estimating Long Memory in Volatility

We consider semiparametric estimation of the memory parameter in a model that includes as special cases both long‐memory stochastic volatility and fractionally integrated exponential GARCH (FIEGARCH) models. Under our general model the logarithms of the squared returns can be decomposed into the sum of a long‐memory signal and a white noise. We consider periodogram‐based estimators using a local Whittle criterion function. We allow the optional inclusion of an additional term to account for possible correlation between the signal and noise processes, as would occur in the FIEGARCH model. We also allow for potential nonstationarity in volatility by allowing the signal process to have a memory parameter d^*1/2. We show that the local Whittle estimator is consistent for d^*∈(0,1). We also show that the local Whittle estimator is asymptotically normal for d^*∈(0,3/4) and essentially recovers the optimal semiparametric rate of convergence for this problem. In particular, if the spectral density of the short‐memory component of the signal is sufficiently smooth, a convergence rate of n^2/5−δ for d^*∈(0,3/4) can be attained, where n is the sample size and δ>0 is arbitrarily small. This represents a strong improvement over the performance of existing semiparametric estimators of persistence in volatility. We also prove that the standard Gaussian semiparametric estimator is asymptotically normal if d^*=0. This yields a test for long memory in volatility.     

基于混合分布的中国股票波动风险因素的识别与分析

论文用GARCH模型描述股票的波动特性，应用混合分布对中国上市公司按照股票波动特性进行分组，发现中国上市公司的波动特性可以被分为4个子总体。其中，子总体1主要包含表现异常的公司股票，其他三个子总体的参数向量的相关性相似，风险大小不同。应用列联表法分析和多元logistic模型统计分析发现，非国有股权分散公司、制造业公司相对偏向低风险公司，社会服务业、房地产公司相对偏向高风险公司，制造业的公司（股票）波动的持续性相对较低。混合分布是对股票特性进行分组的良好工具。     

The Efficacy of Neural Networks in Predicting Returns on Stock and Bond Indices*

This paper uses two recently developed tests to identify neglected nonlinearity in the relationship between excess returns on four asset classes and several economic and financial variables. Having found some evidence of possible nonlinearity, it was then investigated whether the predictive power of these variables could be enhanced by using neural network models instead of linear regression or GARCH models. Some evidence of nonlinearity in the relationships between the explanatory variables and large stocks and corporate bonds was found. It was also found that the GARCH models are conditionally efficient with respect to neural network models, but the neural network models outperform GARCH models if financial performance measures are used. In resonance with the results reported for the tests for neglected nonlinearity, it was found that the neural network forecasts are conditionally efficient with respect to linear regression models for large stocks and corporate bonds, whereas the evidence is not statistically significant for small stocks and intermediate-term government bonds. This difference persists even when financial performance measures for individual asset classes are used for comparison.     

Risk of Bayesian Inference in Misspecified Models,and the Sandwich Covariance Matrix

It is well known that, in misspecified parametric models, the maximum likelihood estimator (MLE) is consistent for the pseudo‐true value and has an asymptotically normal sampling distribution with “sandwich” covariance matrix. Also, posteriors are asymptotically centered at the MLE, normal, and of asymptotic variance that is, in general, different than the sandwich matrix. It is shown that due to this discrepancy, Bayesian inference about the pseudo‐true parameter value is, in general, of lower asymptotic frequentist risk when the original posterior is substituted by an artificial normal posterior centered at the MLE with sandwich covariance matrix. An algorithm is suggested that allows the implementation of this artificial posterior also in models with high dimensional nuisance parameters which cannot reasonably be estimated by maximizing the likelihood.     

Asymptotic Efficiency in Parametric Structural Models with Parameter‐Dependent Support

In certain auction, search, and related models, the boundary of the support of the observed data depends on some of the parameters of interest. For such nonregular models, standard asymptotic distribution theory does not apply. Previous work has focused on characterizing the nonstandard limiting distributions of particular estimators in these models. In contrast, we study the problem of constructing efficient point estimators. We show that the maximum likelihood estimator is generally inefficient, but that the Bayes estimator is efficient according to the local asymptotic minmax criterion for conventional loss functions. We provide intuition for this result using Le Cam's limits of experiments framework.     

我国内地公司ADR与原股的外溢效应研究

本文以14家同时发行H股与ADR,6家同时发行B股与ADR的上市公司为样本,利用GARCH(1,1)-MA(1)模型,探讨ADR与原股报酬波动的外溢效应,以了解我国证券市场与美国证券市场的整合程度。结果发现,我国H股与ADR之间存在报酬波动性的双向相关性,B股与ADR之间存在报酬波动性的单向相关性。本文认为,投资主体差异、市场发展程度不同以及汇率制度是三个影响我国市场和美国市场整合程度的主要因素。     

中国股票市场的信息反应曲线和股票价格波动的非对称性

股票价格波动对于市场信息的反应过程具有非对称性。通过利用多种非对称性GARCH 模型,描述和检验了沪市股票日收益率序列的条件波动性,并通过对股票市场信息影响曲线的分析,发现沪市股票价格波动中存在显著的非对称性反应。这说明股市波动对于不同的政策干预和信息冲击具有不同程度的反应,“利好消息”对股市的刺激作用仍然需要其他市场干预的配合才能发挥出来。     

基于GARCH模型和SV模型的VaR 比较

简单介绍了VaR 的含义及计算方法,指出推测市场因子的波动情况是计算VaR 的关 键. 通过对比GARCH 和SV 模型,得出SV 模型更能刻画金融市场的实际特征. 将随机波动SV 模型应用于VaR 的计算,最后作实证研究. 通过与GARCH 模型下的结果对比,说明基于SV 模 型计算的VaR 更具有动态性和准确性,VaR 更贴切地反映了金融市场的风险水平     

Nonstationary Binary Choice

This paper develops an asymptotic theory for time series binary choice models with nonstationary explanatory variables generated as integrated processes. Both logit and probit models are covered. The maximum likelihood (ML) estimator is consistent but a new phenomenon arises in its limit distribution theory. The estimator consists of a mixture of two components, one of which is parallel to and the other orthogonal to the direction of the true parameter vector, with the latter being the principal component. The ML estimator is shown to converge at a rate of n^3/4 along its principal component but has the slower rate of n^1/4 convergence in all other directions. This is the first instance known to the authors of multiple convergence rates in models where the regressors have the same (full rank) stochastic order and where the parameters appear in linear forms of these regressors. It is a consequence of the fact that the estimating equations involve nonlinear integrable transformations of linear forms of integrated processes as well as polynomials in these processes, and the asymptotic behavior of these elements is quite different. The limit distribution of the ML estimator is derived and is shown to be a mixture of two mixed normal distributions with mixing variates that are dependent upon Brownian local time as well as Brownian motion. It is further shown that the sample proportion of binary choices follows an arc sine law and therefore spends most of its time in the neighborhood of zero or unity. The result has implications for policy decision making that involves binary choices and where the decisions depend on economic fundamentals that involve stochastic trends. Our limit theory shows that, in such conditions, policy is likely to manifest streams of little intervention or intensive intervention.     

双因子非对称已实现SV模型及其实证研究

在基本的SV模型中引入包含丰富日内高频信息的已实现测度,同时考虑其偏差修正以及波动率非对称性与长记忆性,构建了双因子非对称已实现SV（2FARSV）模型.进一步基于连续粒子滤波算法,给出了2FARSV模型参数的极大似然估计方法.蒙特卡罗模拟实验表明,给出的估计方法是有效的.采用上证综合指数和深证成份指数日内高频数据计算已实现波动率（RV）和已实现极差波动率（RRV）,对2FARSV模型进行了实证研究.结果表明：RV和RRV都是真实日度波动率的有偏估计（下偏）,但RRV相比RV是更有效的波动率估计量;沪深股市具有强的波动率持续性以及显著的波动率非对称性（杠杆效应与规模效应）;2FARSV模型相比其它已实现波动率模型具有更好的数据拟合效果,该模型能够充分地捕获沪深股市波动率的动态特征（时变性、聚集性、非对称性与长记忆性）.     

基于GARCH模型和SV模型的VaR 比较

简单介绍了VaR的含义及计算方法,指出推测市场因子的波动情况是计算VaR的关键.通过对比GARCH和SV模型,得出SV模型更能刻画金融市场的实际特征.将随机波动SV模型应用于VaR的计算,最后作实证研究.通过与GARCH模型下的结果对比,说明基于SV模型计算的VaR更具有动态性和准确性,VaR更贴切地反映了金融市场的风险水平.