统计极值理论及其应用研究进展

0引言在我国证券市场,受国家宏观经济调控政策和国际金融市场等因素的影响,金融资产价格会出现一定程度的波动。尤其是股票市场,对调控政策和国际相关行业信息更为敏感。受这些市场信息的影响,股票价格可能产生巨幅波动,从而使投资者面临巨大损失的风险。在这种情况下,如何合理     

基于波动非对称性的中国股市监管研究

文章以1997年1月2日至2007年12月28日上海证券市场综合指数为样本,根据股指波动情况,划分为三个阶段,运用EGARCH和TARCH模型实证研究中国股票市场价格波动的非对称性,分析股票市场波动非对称性的生成机理,提出基于股市波动非对称性政府监管的基本原则,为政府监管股票市场、制定股票市场发展规划与政策,提供具有一般性意义的分析思路和模式,为投资者预测并规避风险提供决策依据.     

中国股市的弱式有效性检验

证券市场(股票市场)的效率一直是证券市场的监管机构和参与者各方关注的问题。对我国证券市场的有效性研究以及关于我国股票市场是否属于强式有效市场、半强式有效市场或弱式有效市场的争论仍在继续。文章侧重于价格的时间序列相关性研究,主要进行了游程检验、序列相关性检验和灵敏性检验。经过实证检验,认为我国股市已经具备弱式有效性。     

股指期货与我国股市的波动性及其交易效率的实证检验

文章针对沪深300指数日收盘数据尖峰、肥尾、偏态特征,利用似然比检验选取广义误差分布作为TGARCH模型扰动分布形式,并在此基础上利用ARMA-TGARCH模型实证检验了股指期货推出对我国股市波动性和交易效率的影响.结果表明:(1)股指期货推出降低了股市的波动性,减少了市场风险;(2)波动干扰信息能够更快地反应到现货市场中,改善了股市的交易效率(3)股指期货推出后,波动非对称性有所减弱,但杠杆效应统计检验不显著.以上结论说明我国股指期货虽然上市时间不长,但它的推出加速了信息的传递速度,降低了市场风险,对于改善我国股票市场的交易效率有积极作用.但由于上市时间短,与相关法律制度建设、国企改革等方面的联动性有待进一步提升.     

股票价格波动与消费支出——基于分段消费函数的研究

文章在考察股票市场波动与家庭持有股票比例关系基础上,利用一个分段的消费函数模型对股票市场波动与消费支出之间的关系进行实证研究.结果表明股票指数是影响家庭财富持有形式的重要因素,并且在不同阶段股市的财富效应也不同,股市发展初期主要是挤占效应,而股市发展到一定阶段财富效应开始发挥作用,这一结论对当前金融危机背景下维持资本市场稳定提供有力证明.     

基于ARCH类模型的中国股市波动性研究

波动性是股票市场最为重要的特性之一,准确描述并掌握股市波动的时变特性有着重要的意义。国内外研究是以股票价格(指数)来刻画市场的波动性,中国股市“量为价先”的运行特点尤为明显,因此笔者试图通过股市成交量来描述股市波动性,希望能对相关研究从另一个角度打开突破口。     

预期引导、政策冲击与股市波动——基于文本分析法的异质性诊断

防范股票市场异常波动是维护金融稳定和防控金融风险的关键一环。货币政策实践中,预期引导与政策冲击对股市波动的实际影响和传导机制迥然不同。现有文献对两者之于股票市场波动 的异质性影响多有讨论,但分歧明显。基于2005年到2019年中国人民银行各季度《货币政策执行报告》和《货币政策大事记》,本文分别构建表征货币政策预期引导强度和实际操作频度的代理变量,对上述指标之于同期A股市场主要行业指数的波动性影响做了多维诊断和系统梳理。研究发现,第一,预期引导效应和政策冲击效应对于股票市场波动性的影响存在显著异质性特征,预期引导有助于平抑市场波动,而频繁调控则会放大股市波动。第二,预期引导的明确性会制约其对股市波动的平缓作用,货币调控意愿的表达越明确,越有助于平抑股票市场波动;而更坚决的“严厉型”表述比态度相对温和的“温和型”表述能够更显著地平抑股票市场波动。第三,实际操作频度对股市波动的放大作用受制于具体调控方向,宽松型调控的频率上升仅会小幅放大股市波动,而紧缩型货币调控则会大幅抬升股市波动性。由此,从平抑股市异常波动、维持金融稳定的角度出发,强化货币政策的预期引导比相机抉择的频繁调控更为重要;在预期引导过程中,应当增强调控意愿表达的明确性和坚决性,以限制其对金融市场运行带来的扰动。     

同业拆借市场与股票市场关系的实证

我国股市属于新兴市场,股市波动较大,市场效率不高,表现为一定程度上的资金拉动型.股票价格取决于未来收益和贴现率,其中影响股票收益的很重要的一个因素是利率.在我国市场化程度最高的是同业拆借市场利率,因此同业拆借市场就成为联接货币市场的重要通道.研究两者之间的互动关系,不仅有助于解释股市收益与波动,而且关系到货币政策如何影响同业拆借市场和股票市场,进而影响到货币政策效力的发挥.     

货币政策与股票价格波动的灰色关联度

我国目前货币市场正面临逐步开放,利率市场化的大环境;资本市场同样面临着对外开放,增加金融产品的发展问题.货币市场和资本市场的快速发展和开放,对中央银行的货币政策调控提出了挑战.近年来,中央银行是否应该干预证券市场的问题逐渐成为理论界讨论的焦点.研究分析银行利率、货币供给量以及再贴现率等货币政策中间目标对证券市场报酬率的预测能力以及探讨货币政策与证券市场报酬之间的关联性,进而判断货币政策是否可以解释证券市场的波动以及货币政策对证券市场的影响程度,对于中央银行制定正确的货币政策;证券监管部门对证券市场的科学监管,防止证券市场剧烈波动;投资者根据国家货币政策发展准确把握股票市场变动的脉搏都有着重要的意义.     

CPI的发布对中国股票市场收益率影响的实证研究——以上海股票市场为例

在引起股票市场波动的众多因素中，消费价格指数CPI日渐引起人们的关注。本文采用事件研究法，以上海证券市场为例。重点研究CPI这一宏观经济信息的公布对中国股票市场的短期影响效应。结果发现，在CPI公布前较短的时间内，股票市场出现显著的异常收益，这表明中国股市有效性不足，重要的经济信息发布前可能存在泄露问题．事后股市对信息的消化吸收也相对缓慢。在稍长的事件期内，CPI信息的发布对股市的累积公告效应较小．市场主体预期的调整和多空双方力量的对比抵消了各事件日内股市受到的信息的冲击。     

Robust estimation of extremes

We consider the problem of making inferences about extreme values from a sample. The underlying model distribution is the generalized extreme-value (GEV) distribution, and our interest is in estimating the parameters and quantiles of the distribution robustly. In doing this we find estimates for the GEV parameters based on that part of the data which is well fitted by a GEV distribution. The robust procedure will assign weights between 0 and 1 to each data point. A weight near 0 indicates that the data point is not well modelled by the GEV distribution which fits the points with weights at or near 1. On the basis of these weights we are able to assess the validity of a GEV model for our data. It is important that the observations with low weights be carefully assessed to determine whether diey are valid observations or not. If they are, we must examine whether our data could be generated by a mixture of GEV distributions or whether some other process is involved in generating the data. This process will require careful consideration of die subject matter area which led to the data. The robust estimation techniques are based on optimal B-robust estimates. Their performance is compared to the probability-weighted moment estimates of Hosking et al. (1985) in both simulated and real data.     

Spatial modeling of extreme rainfall in northeast Thailand

It is well recognized that the generalized extreme value (GEV) distribution is widely used for any extreme events. This notion is based on the study of discrete choice behavior; however, there is a limit for predicting the distribution at ungauged sites. Hence, there have been studies on spatial dependence within extreme events in continuous space using recorded observations. We model the annual maximum daily rainfall data consisting of 25 locations for the period from 1982 to 2013. The spatial GEV model that is established under observations is assumed to be mutually independent because there is no spatial dependency between the stations. Furthermore, we divide the region into two regions for a better model fit and identify the best model for each region. We show that the regional spatial GEV model reflects the spatial pattern well compared with the spatial GEV model over the entire region as the local GEV distribution. The advantage of spatial extreme modeling is that more robust return levels and some indices of extreme rainfall can be obtained for observed stations as well as for locations without observed data. Thus, the model helps to determine the effects and assessment of vulnerability due to heavy rainfall in northeast Thailand.     

Multivariate modelling of spatial extremes based on copulas

To model extreme spatial events, a general approach is to use the generalized extreme value (GEV) distribution with spatially varying parameters such as spatial GEV models and latent variable models. In the literature, this approach is mostly used to capture spatial dependence for only one type of event. This limits the applications to air pollutants data as different pollutants may chemically interact with each other. A recent advancement in spatial extremes modelling for multiple variables is the multivariate max-stable processes. Similarly to univariate max-stable processes, the multivariate version also assumes standard distributions such as unit-Fréchet as margins. Additional modelling is required for applications such as spatial prediction. In this paper, we extend the marginal methods such as spatial GEV models and latent variable models into a multivariate setting based on copulas so that it is capable of handling both the spatial dependence and the dependence among multiple pollutants. We apply our proposed model to analyse weekly maxima of nitrogen dioxide, sulphur dioxide, respirable suspended particles, fine suspended particles, and ozone collected in Pearl River Delta in China.     

The Kumaraswamy GEV distribution

The popular generalized extreme value (GEV) distribution has not been a flexible model for extreme values in many areas. We propose a generalization – referred to as the Kumaraswamy GEV distribution – and provide a comprehensive treatment of its mathematical properties. We estimate its parameters by the method of maximum likelihood and provide the observed information matrix. An application to some real data illustrates flexibility of the new model. Finally, some bivariate generalizations of the model are proposed.     

Modelling conditional variance function in industrial data: A case study

We study the suitability of different modelling methods for joint prediction of mean and variance based on large data sets. We review the approaches to the modelling of conditional variance function that are capable of handling a problem where conditional variance depends on about 10 explanatory variables and training dataset consists of 100 000 observations. We present a promising approach for neural network modelling of mean and dispersion. We compare different approaches in predicting the mechanical properties of steel in two case data sets collected from the production line of a steel plate mill. As a conclusion we give some recommendations concerning the modelling of conditional variance in large datasets.     

Weak convergence for the conditional distribution function in a Koziol–Green model under dependent censoring

In this paper we consider the conditional Koziol–Green model of Braekers and Veraverbeke [2008. A conditional Koziol–Green model under dependent censoring. Statist. Probab. Lett., accepted for publication] in which they generalized the Koziol–Green model of Veraverbeke and Cadarso Suárez [2000. Estimation of the conditional distribution in a conditional Koziol–Green model. Test 9, 97–122] by assuming that the association between a censoring time and a time until an event is described by a known Archimedean copula function. They got in this way, an informative censoring model with two different types of informative censoring. Braekers and Veraverbeke [2008. A conditional Koziol–Green model under dependent censoring. Statist. Probab. Lett., accepted for publication] derived in this model a non-parametric Koziol–Green estimator for the conditional distribution function of the time until an event, for which they showed the uniform consistency and the asymptotic normality. In this paper we extend their results and prove the weak convergence of the process associated to this estimator. Furthermore we show that the conditional Koziol–Green estimator is asymptotically more efficient in this model than the general copula-graphic estimator of Braekers and Veraverbeke [2005. A copula-graphic estimator for the conditional survival function under dependent censoring. Canad. J. Statist. 33, 429–447]. As last result, we construct an asymptotic confidence band for the conditional Koziol–Green estimator. Through a simulation study, we investigate the small sample properties of this asymptotic confidence band. Afterwards we apply this estimator and its confidence band on a practical data set.     

Modelling small and medium enterprise loan defaults as rare events: the generalized extreme value regression model

A pivotal characteristic of credit defaults that is ignored by most credit scoring models is the rarity of the event. The most widely used model to estimate the probability of default is the logistic regression model. Since the dependent variable represents a rare event, the logistic regression model shows relevant drawbacks, for example, underestimation of the default probability, which could be very risky for banks. In order to overcome these drawbacks, we propose the generalized extreme value regression model. In particular, in a generalized linear model (GLM) with the binary-dependent variable we suggest the quantile function of the GEV distribution as link function, so our attention is focused on the tail of the response curve for values close to one. The estimation procedure used is the maximum-likelihood method. This model accommodates skewness and it presents a generalisation of GLMs with complementary log–log link function. We analyse its performance by simulation studies. Finally, we apply the proposed model to empirical data on Italian small and medium enterprises.     

Adaptive estimators for parameters of the autoregression function of a Markov chain

Suppose we observe an ergodic Markov chain on the real line, with a parametric model for the autoregression function, i.e. the conditional mean of the transition distribution. If one specifies, in addition, a parametric model for the conditional variance, one can define a simple estimator for the parameter, the maximum quasi-likelihood estimator. It is robust against misspecification of the conditional variance, but not efficient. We construct an estimator which is adaptive in the sense that it is efficient if the conditional variance is misspecified, and asymptotically as good as the maximum quasi-likelihood estimator if the conditional variance is correctly specified. The adaptive estimator is a weighted nonlinear least-squares estimator, with weights given by predictors for the conditional variance.     

A wavelet-based approach for modelling exchange rates

This paper proposes a new approach, based on the recent developments of the wavelet theory, to model the dynamic of the exchange rate. First, we consider the maximum overlap discrete wavelet transform (MODWT) to decompose the level exchange rates into several scales. Second, we focus on modelling the conditional mean of the detrended series as well as their volatilities. In particular, we consider the generalized fractional, one-factor, Gegenbauer process (GARMA) to model the conditional mean and the fractionally integrated generalized autoregressive conditional heteroskedasticity process (FIGARCH) to model the conditional variance. Moreover, we estimate the GARMA-FIGARCH model using the wavelet-based maximum likelihood estimator (Whitcher in Technometrics 46:225–238, 2004). To illustrate the usefulness of our methodology, we carry out an empirical application using the daily Tunisian exchange rates relative to the American Dollar, the Euro and the Japanese Yen. The empirical results show the relevance of the selected modelling approach which contributes to a better forecasting performance of the exchange rate series.     

Conditional Correlation Models of Autoregressive Conditional Heteroscedasticity With Nonstationary GARCH Equations

In this article, we investigate the effects of careful modeling the long-run dynamics of the volatilities of stock market returns on the conditional correlation structure. To this end, we allow the individual unconditional variances in conditional correlation generalized autoregressive conditional heteroscedasticity (CC-GARCH) models to change smoothly over time by incorporating a nonstationary component in the variance equations such as the spline-GARCH model and the time-varying (TV)-GARCH model. The variance equations combine the long-run and the short-run dynamic behavior of the volatilities. The structure of the conditional correlation matrix is assumed to be either time independent or to vary over time. We apply our model to pairs of seven daily stock returns belonging to the S&P 500 composite index and traded at the New York Stock Exchange. The results suggest that accounting for deterministic changes in the unconditional variances improves the fit of the multivariate CC-GARCH models to the data. The effect of careful specification of the variance equations on the estimated correlations is variable: in some cases rather small, in others more discernible. We also show empirically that the CC-GARCH models with time-varying unconditional variances using the TV-GARCH model outperform the other models under study in terms of out-of-sample forecasting performance. In addition, we find that portfolio volatility-timing strategies based on time-varying unconditional variances often outperform the unmodeled long-run variances strategy out-of-sample. As a by-product, we generalize news impact surfaces to the situation in which both the GARCH equations and the conditional correlations contain a deterministic component that is a function of time.