稀疏组Lasso Granger因果图模型及应用

辨识序列间的因果联系是时间序列分析的主要任务之一。将Granger因果关系的检验问题转换为变量选择问题,应用稀疏组Lasso方法辨识序列间Granger因果关系的存在性和因果影响的滞后阶数。提出了稀疏组Lasso Granger因果图模型,顶点表示多维时间序列的分量序列,顶点间的有向边表示序列间存在的Granger因果关系,定义了滞后信息矩阵揭示因果影响的滞后信息。数值模拟验证了在各种维数和滞后影响结构的模型下,样本量对估计效果的影响。应用到中国宏观经济数据,进行实证分析的结果表明,稀疏组Lasso Granger因果图方法能够较好地揭示序列间的因果关系结构。     

基于图方法的MA和ARMA模型系数检验

应用图模型方法来讨论传统的MA和ARMA模型,证明了MA和ARMA模型的系数为去掉其他时间序列分量线性效应的条件下的偏相关系数,且利用图模型推断算法提出了一种新的参数估计和检验方法。     

基于状态空间图模型方法的投资组合优化决策

将lasso图理论合并到状态空间模型中,利用条件独立性且通过范数惩罚法对协方差阵进行估计。新方法兼具图模型和动态状态空间模型的优点。最后将该方法应用于欧洲股票市场进行投资组合优化决策,结果表明基于lasso图方法的状态空间模型的投资组合业绩要优于自回归和一般的状态空间模型。     

我国沪深两市股指收益率的EGARCH效应分析

对于股指收益序列的波动情况,国外已经有很多实证研究表明其具有高峰厚尾性、波动集群性及非对称性.我国上海股票市场和深圳股票市场是新兴的股票市场,其发展只有十多年的时间,发展尚不成熟,其价格波动较大,投机因素占很大比例,同国外一些成熟市场相比较,我国的波动性更大.但是,尽管沪市和深市大体上波动特点一致,也同处于一个发展环境下,受同样的国家政策及经济发展的影响,其股指波动特点还是存在一定的差异.本文从实证的角度,采用Nelson(1991)提出的EGARCH模型对两个股票市场的股指收益进行了研究分析.     

股票市场系统性崩盘监测分析

文章使用递归图理论及非线性时间序列突变检测的启发式分割算法对股票市场崩盘前市场内生性结构突变时点的检测问题进行研究。通过对12个发达国家（地区）的金融市场和11个新兴国家（地区）的金融市场的崩盘事件进行分析发现：（1）股票市场崩盘前市场层流性特征值LAM会发生显著的大幅下降;（2）对金融危机期间美国股票市场的LAM序列进行递归分析发现,LAM序列呈现类分形自相似性结构,股票市场崩盘前LAM序列存在相变;（3）在市场崩盘前,市场的内生性结构会连续出现异常突变,且异常突变时点早于市场崩盘2到8个月的时间。     

马尔可夫交易策略研究

目前,马尔可夫链在研究股票市场方面得到了广泛的应用,主要体现在两个方面:一是采用马尔可夫转移矩阵预测股指或个股的走势;二是检验股指运行是否满足马尔可夫性质,并证明中国股市的弱有效性.基于已有的研究,本文通过状态的划分计算出转移矩阵,并讨论转移矩阵的平稳性问题,最后对于马尔可夫链模型的预测应用做实证研究.     

股指期货推出对股指波动率影响的实证研究

文章以沪深300指数期货作为样本,通过建立非对称的GARCH模型,对全样本和子样本分别进行股指期货推出与股指波动率影响的实证研究。结果表明:我国股指期货的推出后,股票市场的波动性并未受到影响。同时,股票市场的杠杆效应减弱了。     

股市危机中股指期货应该限制交易吗——基于2015年股市危机的实证分析

利用上证50、沪深300和中证500股指期货合约及其相应指数的高频数据,克服了传统BEKK和DCC模型的不足,通过建立VECM-DCC-VARMA-AGARCH模型考察股市危机期间中国股指期货市场与股票市场之间的信息传导关系与风险传染效应。研究结果表明,股市危机期间股指期货具有很强的价格引导和风险传染效应,股指期货的持续波动加剧了股票市场的进一步波动。因此,提出风险传染效应与市值规模相关、非对称效应和非预期冲击效应与市值规模负相关、波动的风险传染效应与市值规模正相关。危机时期,应抑制股指期货市场上的过度投机,对股指期货采取限制开仓、提高交易保证金和交易手续费都是正确和切实可行的措施。建议监管当局健全股指期货和股票市场交易制度。     

最小二乘支持向量机在条件异方差模型中的应用

相对于标准的支持向量机,最小二乘支持向量机是将求解二次规划问题转化为求解一组线性方程,从而能提高求解速度。将最小二乘支持向量机和GARCH模型相结合应用于金融时间序列预测中。通过在实际股票市场预测中的比较分析,能够证实所给方法是可行的、有效的。     

贝叶斯因果图的构建与应用

贝叶斯网络及因果图的理论方法都已成为较成熟的分析及决策工具.在贝叶斯网络及因果图理论基础上提出构建贝叶斯因果图(BCM)具有可行性及必要性,既结合了二者的优点同时也回避了二者的缺点.文章给出了从因果图出发构建BCM的几个主要构建步骤及要解决的主要问题,同时以实例描述其构建过程.     

A SINful approach to Gaussian graphical model selection

Multivariate Gaussian graphical models are defined in terms of Markov properties, i.e., conditional independences, corresponding to missing edges in the graph. Thus model selection can be accomplished by testing these independences, which are equivalent to zero values of corresponding partial correlation coefficients. For concentration graphs, acyclic directed graphs, and chain graphs (both LWF and AMP classes), we apply Fisher's z-transform, Šidák's correlation inequality, and Holm's step-down procedure to simultaneously test the multiple hypotheses specified by these zero values. This simple method for model selection controls the overall error rate for incorrect edge inclusion. Prior information about the presence and/or absence of particular edges can be readily incorporated.     

On the Markov Equivalence of Chain Graphs, Undirected Graphs, and Acyclic Digraphs

Graphical Markov models use undirected graphs (UDGs), acyclic directed graphs (ADGs), or (mixed) chain graphs to represent possible dependencies among random variables in a multivariate distribution. Whereas a UDG is uniquely determined by its associated Markov model, this is not true for ADGs or for general chain graphs (which include both UDGs and ADGs as special cases). This paper addresses three questions regarding the equivalence of graphical Markov models: when is a given chain graph Markov equivalent (1) to some UDG? (2) to some (at least one) ADG? (3) to some decomposable UDG? The answers are obtained by means of an extension of Frydenberg’s (1990) elegant graph-theoretic characterization of the Markov equivalence of chain graphs.     

On Block Ordering of Variables in Graphical Modelling

Abstract.  In graphical modelling, the existence of substantive background knowledge on block ordering of variables is used to perform structural learning within the family of chain graphs (CGs) in which every block corresponds to an undirected graph and edges joining vertices in different blocks are directed in accordance with the ordering. We show that this practice may lead to an inappropriate restriction of the search space and introduce the concept of labelled block ordering B corresponding to a family of B - consistent CGs in which every block may be either an undirected graph or a directed acyclic graph or, more generally, a CG. In this way we provide a flexible tool for specifying subsets of chain graphs, and we observe that the most relevant subsets of CGs considered in the literature are families of B -consistent CGs for the appropriate choice of B . Structural learning within a family of B -consistent CGs requires to deal with Markov equivalence. We provide a graphical characterization of equivalence classes of B -consistent CGs, namely the B - essential graphs , as well as a procedure to construct the B -essential graph for any given equivalence class of B -consistent chain graphs. Both largest CGs and essential graphs turn out to be special cases of B -essential graphs.     

金融危机前后内地与香港股市联动性及引导性变化的实证研究

运用协整关系检验、格兰杰因果关系检验和脉冲响应分析,从实证的角度对金融危机前后内地股市与香港股市的联动性及引导性等方面所发生的变化进行分析。结果表明,金融危机使得内地股市与香港股市的联动性得以增强,两地股市从原来的单向因果关系转变为双向因果关系,同时内地股市对香港股市的引导关系从原来的不明显变得极其显著。这些变化对处于一体化过程中的两地股市及正在走向国际化的内地股市具有重要的现实意义。     

Maximum Likelihood Estimation in Gaussian Chain Graph Models under the Alternative Markov Property

Abstract.  The Andersson–Madigan–Perlman (AMP) Markov property is a recently proposed alternative Markov property (AMP) for chain graphs. In the case of continuous variables with a joint multivariate Gaussian distribution, it is the AMP rather than the earlier introduced Lauritzen–Wermuth–Frydenberg Markov property that is coherent with data-generation by natural block-recursive regressions. In this paper, we show that maximum likelihood estimates in Gaussian AMP chain graph models can be obtained by combining generalized least squares and iterative proportional fitting to an iterative algorithm. In an appendix, we give useful convergence results for iterative partial maximization algorithms that apply in particular to the described algorithm.     

基于多元经验模式分解的股票收益与宏观经济关系分析

提出一种基于多元经验模式分解的股票市场收益与宏观经济活动关系的分析方法。通过月度道琼斯指数和美国工业生产指数的联合多元经验模式分解,得到多元金融时间序列的多尺度分量。采用希尔伯特—黄变换和边际谱确定每个尺度的主周期,进而在不同尺度下对多元时间序列进行相关性分析及Granger因果检验。结果表明:股票指数在中、长周期的某些尺度上是工业生产指数的Granger原因,序列之间具有明显的相关性,股票指数领先工业生产指数16个月到32个月不等。     

基于Granger因果图方法的物价水平国际间传递分析

目前,对Granger因果关系的研究大多数采用两变量Granger因果检验法,由于忽视其它重要变量的影响,常会导致虚假因果关系的出现。鉴此,采用Granger因果图模型方法分析中国及其主要贸易伙伴国(地区)间的物价传递,研究结果表明:美国在物价传递中发挥着主导作用,物价国际间传递存在一定的区域效应;除和中国香港地区存在即期因果关系外,中国对主要贸易伙伴国(地区)的物价水平基本无显著影响,中国既无输出通货膨胀也无输出通货紧缩。同时,样本期内中国物价水平呈现明显的外部"输入性"特征。因此,中国政府应采取措施应对国际的物价冲击,同时防范物价输入性引发的风险,以实现中国物价的稳定。     

A Unified Approach to the Characterization of Equivalence Classes of DAGs, Chain Graphs with no Flags and Chain Graphs

Abstract.  A Markov property associates a set of conditional independencies to a graph. Two alternative Markov properties are available for chain graphs (CGs), the Lauritzen–Wermuth–Frydenberg (LWF) and the Andersson–Madigan– Perlman (AMP) Markov properties, which are different in general but coincide for the subclass of CGs with no flags . Markov equivalence induces a partition of the class of CGs into equivalence classes and every equivalence class contains a, possibly empty, subclass of CGs with no flags itself containing a, possibly empty, subclass of directed acyclic graphs (DAGs). LWF-Markov equivalence classes of CGs can be naturally characterized by means of the so-called largest CGs , whereas a graphical characterization of equivalence classes of DAGs is provided by the essential graphs . In this paper, we show the existence of largest CGs with no flags that provide a natural characterization of equivalence classes of CGs of this kind, with respect to both the LWF- and the AMP-Markov properties. We propose a procedure for the construction of the largest CGs, the largest CGs with no flags and the essential graphs, thereby providing a unified approach to the problem. As by-products we obtain a characterization of graphs that are largest CGs with no flags and an alternative characterization of graphs which are largest CGs. Furthermore, a known characterization of the essential graphs is shown to be a special case of our more general framework. The three graphical characterizations have a common structure: they use two versions of a locally verifiable graphical rule. Moreover, in case of DAGs, an immediate comparison of three characterizing graphs is possible.     

A Nonparametric Test for Granger Causality in Distribution With Application to Financial Contagion

This article introduces a kernel-based nonparametric inferential procedure to test for Granger causality in distribution. This test is a multivariate extension of the kernel-based Granger causality test in tail event. The main advantage of this test is its ability to examine a large number of lags, with higher-order lags discounted. In addition, our test is highly flexible because it can be used to identify Granger causality in specific regions on the distribution supports, such as the center or tails. We prove that the test converges asymptotically to a standard Gaussian distribution under the null hypothesis and thus is free of parameter estimation uncertainty. Monte Carlo simulations illustrate the excellent small sample size and power properties of the test. This new test is applied to a set of European stock markets to analyze spillovers during the recent European crisis and to distinguish contagion from interdependence effects.     

中国股指期货与股票现货市场之间的风险传递效应研究

 为探索股指期货市场与股票现货市场之间的风险传递效应,本文从日间交易信息和隔夜信息两个角度对沪深300股指期货市场和沪深300指数现货市场进行了实证研究。实证结果显示：股指期货市场与股票现货市场之间的风险传递是双向的,股票现货对股指期货的风险溢出要大于股指期货对股票现货的风险溢出;并且,一市场收益对另一市场收益的影响具有正向杠杆效应,一市场风险对另一市场风险的冲击却具有反向杠杆效应;此外,尽管只有股指期货市场的隔夜信息对其日间收益具有预测能力,但任一市场的隔夜信息对另一市场的日间波动均存在显著的冲击效应。