含趋势项时间序列持久性变点监测

针对核加权方差比率统计量不是监测从非平稳向平稳变化持久性变点一致方法的问题,通过引进一个窗宽参数,提出了一种滑动核加权方差比率统计量来监测含趋势项时间序列从非平稳向平稳变化的持久性.在非平稳原假设下给出了监测统计量的极限分布和经验临界值表,在备择假设下证明了新方法的一致性.模拟结果表明新方法具有比原方法更高的势和更短的平均运行长度,最后通过分析人民币与美元汇率数据进一步说明了该方法的有效性.     

线性回归模型参数变点的在线监测

在线监测金融时间序列并尽早发现变点,对减小金融风险有重要的意义. 通过引进一个窗宽参数,对线性回归模型系数变点提出了一种改进的在线监测方法,并将此方法进一步 用于模型方差变点的监测.在无变点的原假设下给出了监测统计量的渐近分布及经验临界值 表,在备择假设下证明了该方法的一致性.模拟结果表明新方法比已有的方法势高且平均运行 长度短,最后通过两组股票价格变点监测的实例, 进一步说明了该方法的有效性.     

基于小波的非参数回归模型均值变点的Bootstrap监测

本文首次考虑非参数回归模型均值函数结构变点的在线监测问题. 首先对回归函数的局部线性估计值进行小波变换， 基于得到的小波系数构造监测统计量， 并在原假设和备择假设下推导出监测统计量的渐近分布； 为提高监测效果， 进一步构造了Bootstrap在线监测方法， 定义了停时； 模拟结果和实例分析显示该方法可以很好地监测到变点， 并具有较短的检测延迟.     

基于跳扩散模型的石油价格长期趋势分析

分析了国际石油市场1986至2012年周价格形成机制的长期演变趋势.在讨论均衡理论基础上,以长期市场供求关系解释了国际油价长期波动现象.基于跳扩散模型拟合石油价格动态过程,利用结构变点检验和累积量估计方法进行了实证研究.历史数据分析表明石油价格具有高波动性、高强度跳跃性和上升漂移特征.此外,模型预测即使当前大幅增加石油投资,未来几年内石油价格变化仍会处于一种高频跳跃的上行阶段.     

基于参数递归更新的惯性器件寿命预测

在基于随机滤波理论的剩余寿命预测模型中,模型参数的获取是离线的,且当历史数据较少时,模型参数不能够进行修正,影响了预测精度.针对以上问题,采用递归期望最大化(Recursive Expectation Maximization,REM)算法来对模型参数进行递归更新,提出了基于参数递归更新的剩余寿命实时预测模型.应用实际的监测数据和参数递归更新的寿命预测模型,进行了某导弹陀螺仪的寿命预测实验.仿真结果表明,该预测模型能够根据实时的数据对模型参数进行快速地更新,满足预测的实时性要求.     

基于变点–算术失效强度减的设备维修质量评估

针对设备维修效果评估中存在的失效强度变点问题,给出了一个具有失效变点的算术失效强度减模型.该模型应用幂律模型平滑具有变点的失效强度,进而假设设备经历一次预防维修后的失效强度等于预防维修前的失效强度和一个当量之和.这个当量与预防维修前的失效强度和设备固有失效强度之差成一定比例,并以该比例评价预防维修质量.构建了基于最小二...     

预测沪深股市市场波动性

研究目的在于:首先,检验和对比三种GARCH模型对于我国上海、深圳股市波动性的预测能力.其次,使用非对称的预测指标以体现对于预测误差高低的不同个体需求.在对于4个对称型的预测常规指标中,TGARCH对于2个市场波动的预测结果都是最佳的,而EGARCH的预测结果也要好于GARCH(1,1).这表明我国上海与深圳市场受坏消息的负面影响大于同等程度好消息的正面影响,而运用单边非对称的GARCH模型将更利于提高波动性预测的准确性.在非对称预测指标方面,研究认为EGARCH模型对于那些更愿意低估市场波动性的投资者而言较为有利,而GARCH(1,1)模型则相应满足了希望高估市场波动性的投资者的需求.这也表明投资者应根据自己的需要来选择相应的波动性预测模型.     

连续时间资产收益变结构模型的研究

提出了应用MCMC方法的连续时间变结构模型的单一变结构点的定位方法,并提出了连续时间多变结构点模型的变结构点定位方法;该方法在确定变结构点位置的同时,又能估计相应的模型参数.用该方法对上海股市综合指数的收益序列进行了变结构分析,理论与实证结果表明该方法是有效且可行的.     

季节波动数据特征提取与分数阶灰色预测建模

季节性波动数据具有长期趋势性、季节波动性与局部随机振荡性等复杂特征,这给其预测模型的合理构建造成了难度.文章首先通过排序函数f(x_ik)挖掘季节波动数据中相关元素的序位关系及其演变规律,实现了季节波动数据的特征提取及驱动项的构造.然后通过构建分数阶多变量灰色预测模型FMGM(1,N),实现了其累加阶数从正整数到全体实数的拓展与优化.最后,将FMGM(1,N)应用于具有季节波动性特征的我国GDP月度数据的拟合与预测,建模结果显示其模拟和预测精度优于当前主流的单变量及多变量灰色预测模型、非线性回归模型、Arima模型及智能建模方法(support vector machine,SVM;long short-term memory,LSTM).本研究成果为研究季节波动性数据提供了一种新的预测建模方法,对丰富和完善预测模型方法体系具有积极意义.     

基于广义非线性工具变量法的综列单位根检验

当截面个体之间显著相关时,非线性工具变量法(NIV)综列单位根检验存在严重的分布扭曲.该文基于似无关回归形式的可行广义最小二乘法和非线性工具变量估计方法,提出了广义非线性工具变量法(GNIV)综列单位根检验,以修正NIV检验的分布扭曲. 在存在综列单位根的原假设下,GNIV检验统计量的极限分布为标准正态分布,而在备选假设下则趋向于负无穷大. 仿真实验结果显示,在截面个体之间显著相关时,GNIV检验的有限样本性质显著优于Chang的NIV检验和Pesaran的CIPS检验.     

OPTIMAL AND ROBUST DETECTION OF MULTIVARIATE OUTLIERS FOR ELLIPTICALLY CONTOURED DISTRIBUTION

The outlier problem for a multivariate elliptically contoured distribu-tion's random sample with mean slippage is defined and the likelihood ratio test ofthe null hypothesis,in which there are no outliers,versus the alternative hypothesis,in which some outliers are present,is derived.We show that the testing problemis invariant under a group of affine transformations and obtain the maximal in-variance which is equivalent to the likelihood ratio testing statistic.Furthermore,the non-null and null density distribution functions of the likelihood ratio testingstatistic are derived.We find that the null density distribution function of thetesting statistic is robust and the density distribution function is a monotonicallikelihood ratio function of the maximal invariance.Therefore,the likelihood ratiotest is a uniformly most powerful invariant test among the group of affine transfor-mations.In the last section,we give an example of detecting multivariate outliersin elliptically contoured distribution.     

Test on Stochastic Block Model: Local Smoothing and Extreme Value Theory

In this paper, to obtain a consistent estimator of the number of communities, the authors present a new sequential testing procedure, based on the locally smoothed adjacency matrix and the extreme value theory. Under the null hypothesis, the test statistic converges to the type I extreme value distribution, and otherwise, it explodes fast and the divergence rate could even reach n in the strong signal case where n is the size of the network, guaranteeing high detection power. This method is simple to use and serves as an alternative approach to the novel one in Lei (2016) using random matrix theory. To detect the change of the community structure, the authors also propose a two-sample test for the stochastic block model with two observed adjacency matrices. Simulation studies justify the theory. The authors apply the proposed method to the political blog data set and find reasonable group structures.

     

Regression Function Comparison for Paired Data

In this paper, the regression function comparison for paired data is studied. The proposed test statistic is based on the weighted integral of characteristic function marked by the difference of responses. There are several merits of the proposed statistic. For instance, it takes a simple V-statistic form. No bandwidth is needed. No moment conditions are required for covariates. It can be applied to covariates of any fixed dimension. The asymptotic results are also developed. It is proven that n times the proposed test statistic converges to a finite limit under the null hypothesis and the test is consistent against any fixed alternatives. Local alternative hypotheses which converge to the null hypothesis at the rate of n-1/2 are also detected. A suitable Bootstrap algorithm is also proposed for the implementation of the proposed test statistic. Simulation studies are carried out to illustrate the merits of the proposed method. A real data example is also used to illustrate the proposed testing procedures.     

Rank-Based Test for Partial Functional Linear Regression Models

This paper investigates the hypothesis test of the parametric component in partial functional linear regression models. Based on a rank score function, the authors develop a rank test using functional principal component analysis, and establish the asymptotic properties of the resulting test under null and local alternative hypotheses. A simulation study shows that the proposed test procedure has good size and power with finite sample sizes. The authors also present an illustration through fitting the Berkeley Growth Data and testing the effect of gender on the height of kids.     

Consistency of Chi-Squared Test with Varying Number of Classes

The classical chi-squared goodness of fit test assumes the number of classes is fixed,meanwhile the test statistic has a limiting chi-square distribution under the null hypothesis.It is well known that the number of classes varying with sample size in the test has attached more and more attention.However,in this situation,there is not theoretical results for the asymptotic property of such chi-squared test statistic.This paper proves the consistency of chi-squared test with varying number of classes under some conditions.Meanwhile,the authors also give a convergence rate of KolmogorovSimirnov distance between the test statistic and corresponding chi-square distributed random variable.In addition,a real example and simulation results validate the reasonability of theoretical result and the superiority of chi-squared test with varying number of classes.     

风险中性高阶矩:特征、风险与应用

本文采用香港恒生指数期权中的虚值期权计算香港股票市场风险中性高阶矩, 通过其与另一种高阶矩预期——运用历史分布通过AR(1)-GARCH(1,1)模型估计出来的现实世界高阶矩预期之间的关系分析高阶矩风险溢酬.研究结果发现: 在香港股票市场中,偏度、峰度等高阶矩具有非常显著的风险溢酬, 且风险溢酬均小于0. 这表明香港市场的投资者热衷于冒险, 以在短时间内获得较大收益.另外,考察了香港股票市场的期权价格结构,我们发现从恒生指数期权中得到的香港股票市场隐含波动率几乎是一条水平的直线. 在对香港市场整体高阶矩进行分析时,也发现其偏度与峰度不能拒绝市场整体分布为正态分布的假设.     

周期异方差时间序列中季节单位根的Gauss 检验

为检验带异方差的季节时间序列中的单位根,提出了基于Cauchy估计的Zc统计量.在原假设下得到该检验统计量的极限分布服从于标准正态分布,并与季节周期d和误差项的周期异方差无关.Monte Carlo模拟计算表明当模型中自回归系数接近1时,用该方法得到的估计值比普通的最小二乘方法得到的估计值误差小.计算结果和实例分析结果表明了用该方法检验季节单位根的简便性和有效性.     

Inference on coefficient function for varying-coefficient partially linear model

One important model in handling the multivariate data is the varying-coemcient partially linear regression model.In this paper,the generalized likelihood ratio test is developed to test whether its coefficient functions are varying or not.It is showed that the normalized proposed test follows asymptoticallyχ~2-distribution and the Wilks phenomenon under the null hypothesis,and its asymptotic power achieves the optimal rate of the convergence for the nonparametric hypotheses testing.Some simulation studies illustrate that the test works well.