GARCH模型对上海股市的一个实证研究

GARCH模型是近20年发展起来的时间序列模型，它反映了经济变量之间特殊的不确定形式：方差随时间变化而变化，所以其在金融市场的预测与决策方面有着重要的作用。本文详细介绍了GARCH模型以及其主要变形，并建立了基于t分布和正态分布假设的GARCH（1，1）模型对股票市场进行了风险分析。结果表明，基于t分布的假设能更准确地拟和GARCH（1，1）模型。     

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。     

日交易量与股票日收益GARCH效应

本文利用中国股票市场的48只具有代表性的股票，对股票日收益的GARCH效应进行了实证研究。结果表明，对于交易活跃的市场，股票日交易量可以很好的解释股票日收益的GARCH效应，当在GARCH模型中引入日交易量作为解释变量，我们发现GARCH效应显著降低，但依然显著存在。     

基于Expectile和Realized GARCH模型的波动率预测

Realized GARCH模型是预测波动率的经典模型之一,最小化非对称二次损失函数的Expectile对收益率尾部分布更加敏感,我们在Realized GARCH模型的基础上引入Expectile提出Expectile-Realized GARCH模型。以沪深300指数的高频收益率为例建模分析,对比不同模型下的波动率预测效果,发现Expectile-Realized GARCH模型较Realized GARCH模型对波动率预测能力更好。其中,当风险水平为95%时,对应的Expectile-Realized GARCH波动率预测能力最好。     

极值理论在风险度量中的应用--基于上证180指数

精确度量风险是金融风险管理的关键问题。本引入广义帕雷托分布代替传统的正态分布等，精确描述金融收益的厚尾特征。并将基于广义帕雷托分布的VaR模型和其它模型方法，如GARCH(1，1)、GARCH(1，1)-t、历史模拟法、方差-协方差方法，进行比较分析。实证研究表明，基于广义帕雷托分布的VaR模型比传统的模型方法更适合厚尾分布高分位点的预测，并且其预测结果比较稳定。这使得基于广义帕雷托分布的VaR模型成为VaR度量方法中最稳健的方法之一。     

深证成指周收益率波动性的实证研究

利用GARCH模型,对深圳成分指数的周收益率波动性进行了实证研究。以深证成指周收盘数据建立了GARCH模型,利用估计出的GARCH模型得到深证成指周收益率序列的条件方差的估计值,预测出深证成指周收益率序列未来若干期的条件方差。结果表明,深证成指周收益率序列的波动性可以用GARCH模型进行很好的拟合。     

基于损失函数的GARCH类模型波动率预测评价

本文的目的是通过利用多种损失函数评估三种GARCH模型的预测精度，找到最优的股指期货日内波动率研究预测模型。利用之前的研究结果，三个沪深300股指期货日内一分钟日内收益率被用作研究对象，对标准GARCH,eGARCH以及RealGARCH三个模型做了实证检验，并利用多种损失函数，从不同角度衡量三个波动率模型的预测精度。研究发现：Sample1样本的RealGARCH模型有最好的预测效果，而Sample2样本与Sample6样本的eGARCH模型有最好的预测精度。因此，在对沪深300股指期货日内波动率研究时，应根据其样本特征，优先选择具有能够反映非对称特征的波动率模型来刻画波动过程，对未来波动率做预测。     

GARCH过程的同期聚合

我们首先提出由独立一元变量GARCH过程的同期聚合可得到一个弱GARCH过程 (见Drost和Nijman( 1 993) )过程 ,接着分析同期聚合的参数同原始过程参数间的相依性 ,指出聚合后方差参数依赖于原始方差和参数的峰度 .     

马尔科夫状态转换GARCH模型的波动持续性研究——对估计方法的探讨

由于GARCH模型的系数固定不变,不能反映金融市场波动的结构变化,所以对于波动预测和动态风险管理都还不够完善。本文在GARCH模型中引入马尔科夫过程,从而使状态的转换体现在GARCH模型中,通过设置状态变量,构建马尔科夫状态转换GARCH模型(MRSGARCH),从而较好地揭示了存在结构转换的波动特性,对MRSGARCH模型进行参数估计,并给出了预测的详细过程,最后提出了MRSGARCH的波动持续性的估计方法。     

基于GARCH模型的中美汇率实证分析

汇率制度改革后,加强人民币汇率风险管理已成为摆在各大经济主体面前的重大课题.基于2010年1月1日至2012年5月10日的美元对人民币日汇率值,利用广义条件异方差自回归(GARCH)模型,对中美汇率日数据进行处理与检验,得到了残差存在异方差性.在此基础上建立了汇率GARCH模型,实证分析表明精确性高.     

On the fixing of values of sequences of seminorms

Theorems on the fixing of values of sequences of continuous seminorms on certain sets in Banach spaces are proved, enabling one to obtain new results on the asymptotic behavior of approximations of individual functions and on the convergence of interpolation processes on classes of functions.Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 44, No. 4, pp. 467–474, April, 1992.     

A new class of operators and a description of adjoints of composition operators

Starting with a general formula, precise but difficult to use, for the adjoint of a composition operator on a functional Hilbert space, we compute an explicit formula on the classical Hardy Hilbert space for the adjoint of a composition operator with rational symbol. To provide a foundation for this formula, we study an extension to the definitions of composition, weighted composition, and Toeplitz operators to include symbols that are multiple-valued functions. These definitions can be made on any Banach space of analytic functions on a plane domain, but in this work, our attention is focused on the basic properties needed for the application to operators on the standard Hardy and Bergman Hilbert spaces on the unit disk.     

Experimental determination of the life of oriented molecules of higher fatty acids under conditions of surface friction of polymers against steel

It is shown that the life of boundary lubricants is much greater on polymers than on steel, and a hypothesis is put forward, and experimentally confirmed, to explain the causes of the breakdown of boundary lubricants on polymer and steel surfaces.Mekhanika Polimerov, Vol. 1, No. 5, pp. 101–106, 1965     

一类初等微分几何定理机器证明的算法与实现

空间曲面上的曲线论是初等微分几何的重要部分．作者提出了一种以外微分运算和向量计算为主要工具,可以进行有关曲面上曲线局部性质的定理机器证明的算法．该算法结合了曲面上的活动标架,曲面上曲线的测地标架和曲线自身的Frenet标架,在Maple 9下得到实现．对20个例子进行的测试表明,由该算法生成的自动证明简短可读．     

Behavior of zeros of polynomials of near best approximation

The purpose of this paper is to study the asymptotic behavior of the zeros of polynomials of near best approximation to continuous functions f on a compact set E in the case when f is analytic on the interior of E but not everywhere on the boundary. For example, suppose E is a finite union of compact intervals of the real line and f is a continuous function on E, but is not analytic on E; then we show (cf. Corollary 2.2) that every point of E is a limit point of zeros of the polynomials of best uniform approximation to f on E. This fact answers a question posed by P. Borwein who showed that, for the case when E is a single interval and f is real-valued, then the above hypotheses on f imply that at least one point of E is the limit point of zeros of such polynomials.     

Estimate of the Order of Growth of a Class of Entire Functions on the Real Axis

For a class of entire functions we study the problem of estimation of the order of growth of functions on the real axis. This problem is important for the justification of the integral representation of bounded solutions to certain partial differential equations considered in other papers of the authors. In order to obtain an estimate of the order of growth of a function on the real axis, we use the method of differential equations. The method is based, on one hand, on the construction of a system of first-order ordinary differential equations whose solution is a vector function of traces of function and its derivatives on the real axis. On the other hand, under the respective change of variables in the system of equations, we obtain an estimate of the solution to the system of equations for a large positive values of the argument. The obtained estimate is non-trivial and shows the way a complex parameter of a power series affects the order of growth of a function.     

On the number of essential arguments of homomorphisms between products of median algebras

In this paper we characterize classes of median-homomorphisms between products of median algebras, that depend on a given number of arguments, by means of necessary and sufficent conditions that rely on the underlying algebraic and on the underlying order structure of median algebras. In particular, we show that a median-homomorphism that take values in a median algebra that does not contain a subalgebra isomorphic to the m-dimensional Boolean algebra as a subalgebra cannot depend on more than \(m-1\) arguments. In view of this result, we also characterize the latter class of median algebras. We also discuss extensions of our framework on homomorphisms over median algebras to wider classes of algebras.     

Nonexistence of nonnegative solutions of elliptic systems of divergence type

In this paper we deal with noncoercive elliptic systems of divergence type, that include both the p-Laplacian and the mean curvature operator and whose right-hand sides depend also on a gradient factor. We prove that any nonnegative entire (weak) solution is necessarily constant. The main argument of our proofs is based on previous estimates, given in Filippucci (2009) [12] for elliptic inequalities. Actually, the main technique for proving the central estimate has been developed by Mitidieri and Pohozaev (2001) [23] and relies on the method of test functions. No use of comparison and maximum principles or assumptions on symmetry or behavior at infinity of the solutions are required.     

On domains of regularity of the solutions of some special classes of Monge-Ampère-type equations

We present several results on estimates from above of the regularity domains for special classes of solutions to Monge-Ampère-type equations (in particular, periodic at least in one variable). Also, we present some geometrical and geophysical applications. Namely, we are concerned with the problem on dimensions of a single-valued projection on a plane of a surface with separated-from-zero negative Gaussian curvature and discuss the existence or nonexistence of a solution to the pressure-wind balance equation on a torus. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 12, No. 1, pp. 237–246, 2006.     

A local estimate of the maximum of the module of the deviator of the strain tensor in an elastoplastic body with linear hardening

An upper estimate for the module of the deviator of the strain tensor at any interior point of an elastoplastic body is proved. It depends only on the L₂-norm of the deviator of the strain tensor over the domain occupied by this elastoplastic body, on the L_p-norm of body forces, on the parameters of the elastoplastic medium, and on the distance to the boundary of the body. Bibliography: 5 titles. To dear Olga Alexandrovna Ladyzhenskaya on her jubilee Translated fromZapiski Nauchnykh Seminarov POMI, Vol. 200, 1992, pp. 167–176. Translated by G. A. Seregin.