基于GARCH模型的沪深地产股波动性分析及预测

近年来GARCH类模型在预测波动率方面得到了广泛应用,鉴于股票和房地产两个市场对我国经济发展的重要性,所以选择沪深两市地产指数的收益率做波动性研究.丈章运用GARCH类模型对沪深地产指数收益率的波动进行了枯计和预测,结果表明沪深地产指数收益率的波动不存在杠杆效应,投资者投机目的较强,M-Z回归和损失函数评价结果显示,GARCH(1,1)-M模型的样本外预测刚效果是最好的,但不能准确预测非常大的波动.     

基于Wishart检验的金融市场风险溢出研究

在假定两个金融市场均为有效市场的条件下,基于Wishart分布对不同滞后相关系数进行Wishart检验,来确定在这两个金融市场之间的风险溢出发生期和风险溢出强度。实证检验结果显示,沪、深两市之间的风险溢出发生期大约在3分钟之内,且在3分钟的风险溢出发生期内沪市对深市的风险溢出强度较深市对沪市的风险溢出强度衰减速度缓慢,这反映了沪市较深市具有更重要的影响力,该研究结果与金融市场的实际情况吻合。     

沪深300指数统计特征研究

文章以2005年4月8日至2007年10月30日沪深300指数日收盘价格序列为样本,以复合收益率为研究对象,通过对股市收益率非正态性检验,分析了沪深300指数的一些典型统计特征,验证了沪深300指数收益率"尖峰厚尾"的特性。因此有必要寻找一种更合适的模型,以便更准确地反映沪深300指数收益的真实分布。最后对其进行了GARCH效应的检验,结果表明沪深300指数收益率的波动存在着显著的GARCH效应。     

上证指数收益率的ARCH族模型的实证分析

文章利用ARCH族模型,选取2005～2009年的上证综指日收益率作为对象对我国沪市波动情况进行了实证研究.研究结果表明,我国沪市日收益率序列具有明显的聚集性、波动性、尖峰厚尾的特征,ARCH族模型较好的拟合了上证指数收益率序列.     

基于CAPM模型的上海股票市场适应性检验

文章选取了沪市A股的643只股票从2003-2013年的月收益率数据作为研究对象,将其分为50组,借用Eviews软件采用BJS和Fama-Macbeth方法对收益率进行了时间序列检验和横截面检验,得出CAPM模型无法完全解释股票收益率这一结论,即CAPM理论并不完全适用于上海股票市场.     

上海证券市场基于修正R/S分析的长记忆研究

文章以上证综合指数周收益率和日收益率为研究对象,用R/S分析法和修正R/S分析法来分析上海证券市场的长记忆性,并使用V统计量对其进行双侧检验,此外还分析了R/S分析法产生偏差的原因.得出结论:上证综合指数周收益率时间序列和日收益率时间序列并没有表现出显著的长记忆性.     

基于回归的时变偏度和时变峰度识别检验

资产收益率时变高阶矩建模的首要前提是资产收益率的偏度和峰度具有时变性,即资产收益率存在类似于异方差性的异偏度和异峰度特征。目前文献中的时变偏度和时变峰度识别检验存在适用性较差且检验功效较低等不足。本文提出基于回归的检验方法识别资产收益率偏度和峰度的时变性。该检验一方面利用概率积分变换缓解了拉格朗日乘数检验对资产收益率序列的高阶矩存在性的限制,另一方面考虑了检验统计量中参数估计的不确定性对其统计性质的影响,具有良好的渐近统计性质且适用性更广。蒙特卡洛模拟表明该检验具有良好的有限样本性质,具有合适的检验水平和较高的检验功效。最后,将基于回归的检验运用于上证综指和深圳成指收益率的时变建模研究中。     

基于证券市场信息中介效应的房地产行业研究

房地产和股票是居民财富的主要保有形式,文章基于2009年1月至2011年12月中国住房销售价格指数和沪深两市证券综合指数月度数据对我国房地产市场与证券市场相关性进行研究,结果表明,我国房地产市场与沪市证券市场存在长期协整关系,但与深市证券市场协整关系不显著；从短期来看,证券市场是引致房地产市场的格兰杰原因,但房地产市场不是证券的格兰杰原因.     

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。     

中国股市收益率与波动性长期记忆效应的检验

本文用基于方差的方法、Ro的修正R/S检验、标准GPH法以及tapered GPH法对沪深股市指数收益率及其波动性进行了长记忆性检验.结果表明沪市收益率序列不存在长记忆性,深市收益率序列存在一定的长记忆性;沪深股市的波动性均表现出显著的长记忆性,并且我国股市不存在趋势或结构突变.     

On entropy goodness-of-fit test based on integrated distribution function

In this study, we consider an entropy-type goodness-of-fit (GOF) test based on integrated distribution functions. We first construct the test for the simple vs. simple hypothesis and then extend it to the composite hypothesis case. It is shown that under regularity conditions, the null limiting distribution of the proposed test is a function of a Brownian bridge. A bootstrap method is also considered and is shown to be weakly consistent. A simulation study and real data analysis are conducted for illustration.     

Parameter estimation of the flexible Weibull distribution for type I censored samples

Often in practice one is interested in the situation where the lifetime data are censored. Censorship is a common phenomenon frequently encountered when analyzing lifetime data due to time constraints. In this paper, the flexible Weibull distribution proposed in Bebbington et al. [A flexible Weibull extension, Reliab. Eng. Syst. Safety 92 (2007), pp. 719–726] is studied using maximum likelihood technics based on three different algorithms: Newton Raphson, Levenberg Marquardt and Trust Region reflective. The proposed parameter estimation method is introduced and proved to work from theoretical and practical point of view. On one hand, we apply a maximum likelihood estimation method using complete simulated and real data. On the other hand, we study for the first time the model using simulated and real data for type I censored samples. The estimation results are approved by a statistical test.     

Inference for a leptokurtic symmetric family of distributions represented by the difference of two gamma variates

We introduce a family of leptokurtic symmetric distributions represented by the difference of two gamma variates. Properties of this family are discussed. The Laplace, sums of Laplace and normal distributions all arise as special cases of this family. We propose a two-step method for fitting data to this family. First, we perform a test of symmetry, and second, we estimate the parameters by minimizing the quadratic distance between the real parts of the empirical and theoretical characteristic functions. The quadratic distance estimator obtained is consistent, robust and asymptotically normally distributed. We develop a statistical test for goodness of fit and introduce a test of normality of the data. A simulation study is provided to illustrate the theory.     

A nonparametric approach to detecting the difference of survival medians

Some nonparametric methods have been proposed to compare survival medians. Most of them are based on the asymptotic null distribution to estimate the p-value. However, for small to moderate sample sizes, those tests may have inflated Type I error rate, which makes their application limited. In this article, we proposed a new nonparametric test that uses bootstrap to estimate the sample mean and variance of the median. Through comprehensive simulation, we show that the proposed approach can control Type I error rates well. A real data application is used to illustrate the use of the new test.     

Small Sample Tests for Shape Parameters of Gamma Distributions

The introduction of shape parameters into statistical distributions provided flexible models that produced better fit to experimental data. The Weibull and gamma families are prime examples wherein shape parameters produce more reliable statistical models than standard exponential models in lifetime studies. In the presence of many independent gamma populations, one may test equality (or homogeneity) of shape parameters. In this article, we develop two tests for testing shape parameters of gamma distributions using chi-square distributions, stochastic majorization, and Schur convexity. The first one tests hypotheses on the shape parameter of a single gamma distribution. We numerically examine the performance of this test and find that it controls Type I error rate for small samples. To compare shape parameters of a set of independent gamma populations, we develop a test that is unbiased in the sense of Schur convexity. These tests are motivated by the need to have simple, easy to use tests and accurate procedures in case of small samples. We illustrate the new tests using three real datasets taken from engineering and environmental science. In addition, we investigate the Bayes’ factor in this context and conclude that for small samples, the frequentist approach performs better than the Bayesian approach.     

Estimation of exponential-polynomial distribution by holonomic gradient descent

ABSTRACT

We study the holonomic gradient decent for maximum likelihood estimation of exponential-polynomial distribution, whose density is the exponential function of a polynomial in the random variable. We first consider the case that the support of the distribution is the set of positive reals. We show that the maximum likelihood estimate (MLE) can be easily computed by the holonomic gradient descent, even though the normalizing constant of this family does not have a closed-form expression, and discuss the determination of the degree of the polynomial based on the score test statistic. Then, we present extensions to the whole real line and to the bivariate distribution on the positive orthant.     

On entropy-based goodness-of-fit test for asymmetric Student-t and exponential power distributions

This paper examines the goodness-of-fit (GOF) test for a generalized asymmetric Student-t distribution (ASTD) and asymmetric exponential power distribution (AEPD). These distributions are known to include a broad class of distribution families and are quite suitable to modelling the innovations of financial time series. Despite their popularity, to our knowledge, no studies in the literature have so far investigated their affinity and differences in implementation. To fill this gap, we examine the empirical power behaviour of entropy-based GOF tests for hypotheses wherein the ASTD and AEPD play the role of null and alternative distributions. Our findings through a simulation study and real data analysis indicate that the two distributions are generally hard to distinguish and that the ASTD family accommodates AEPDs to a greater degree than the other way around for larger samples.     

Candidate-gene association analysis for a continuous phenotype with a spike at zero using parent-offspring trios

In this paper, we propose the class of generalized additive models for location, scale and shape in a test for the association of genetic markers with non-normally distributed phenotypes comprising a spike at zero. The resulting statistical test is a generalization of the quantitative transmission disequilibrium test with mating type indicator, which was originally designed for normally distributed quantitative traits and parent-offspring data. As a motivational example, we consider coronary artery calcification (CAC), which can accurately be identified by electron beam tomography. In the investigated regions, individuals will have a continuous measure of the extent of calcium found or they will be calcium-free. Hence, the resulting distribution is a mixed discrete-continuous distribution with spike at zero. We carry out parent-offspring simulations motivated by such CAC measurement values in a screening population to study statistical properties of the proposed test for genetic association. Furthermore, we apply the approach to data of the Genetic Analysis Workshop 16 that are based on real genotype and family data of the Framingham Heart Study, and test the association of selected genetic markers with simulated coronary artery calcification.     

A new extended generalized Gompertz distribution with statistical properties and simulations

Abstract

Statistical distributions are very useful in describing and predicting real world phenomena. In many applied areas there is a clear need for the extended forms of the well-known distributions. Generally, the new distributions are more flexible to model real data that present a high degree of skewness and kurtosis. The choice of the best-suited statistical distribution for modeling data is very important.

In this article, we proposed an extended generalized Gompertz (EGGo) family of EGGo. Certain statistical properties of EGGo family including distribution shapes, hazard function, skewness, limit behavior, moments and order statistics are discussed. The flexibility of this family is assessed by its application to real data sets and comparison with other competing distributions. The maximum likelihood equations for estimating the parameters based on real data are given. The performances of the estimators such as maximum likelihood estimators, least squares estimators, weighted least squares estimators, Cramer-von-Mises estimators, Anderson-Darling estimators and right tailed Anderson-Darling estimators are discussed. The likelihood ratio test is derived to illustrate that the EGGo distribution is better than other nested models in fitting data set or not. We use R software for simulation in order to perform applications and test the validity of this model.     

Analysis of survival data by an exponential-generalized Poisson distribution

In this paper, we consider the distribution of life length of a series system with random number of components, say Z. Considering the distribution of Z as generalized Poisson, an exponential-generalized Poisson (EGP) distribution is developed. The generalized Poisson distribution is a generalization of the Poisson distribution having one extra parameter. The structural properties of the resulting distribution are presented and the maximum likelihood estimation of the parameters is investigated. Extensive simulation studies are carried out to study the performance of the estimates. The score test is developed to test the importance of the extra parameter. For illustration, two real data sets are examined and it is shown that the EGP model, presented here, fits better than the exponential–Poisson distribution.