似无关动态协整模型中的水平扭曲与校正

本文在解析似无关动态协整模型及其动态最小二乘估计的基础上,从理论上揭示了关于协整参数的假设检验存在严重的水平扭曲,即对协整参数约束的Wald检验统计量的渐近卡方分布存在严重的有限样本扭曲。进一步,本文应用自举抽样技术对水平扭曲进行了有效校正。基于本文的发现,我们建议在对似无关动态协整模型中的参数进行假设检验时,为保证结论的准确性,应使用自举抽样推断技术产生统计量值并由此来形成检验结论。     

偏差修正的预白化HAC法在平稳过程伪回归中的应用

在传统预白化HAC法存在有限样本偏差的基础上,提出将自回归参数偏差修正法和残差调整法来减少预白化HAC法的偏差,从而降低相互独立的平稳过程之间发生伪回归的概率。通过一系列的蒙特卡罗模拟表明：第一修正的预白化HAC法确实减少了伪回归概率,且自回归参数偏差修正法减少的幅度要比残差调整法要大得多;第二相对于同方差情形而言,存在GARCH类异方差的回归中预白化HAC法具有更低的伪回归概率;第三当数据过程是AR(2)过程时,在持久性相同的情况下预白化HAC法的伪回归概率要低于相应的AR(1)数据过程。但在高于2阶的自回归数据过程的回归中,残差调整的预白化HAC的伪回归概率具有优势。在样本容量较大(T≥500)时自回归参数修正的预白化HAC法的伪回归概率很接近检验水平,但残差调整的预白化HAC法具有微弱的向下检验水平扭曲.     

基于MF-VAR的混频数据非线性格兰杰因果关系检验

研究目标：提出一种针对混频数据非线性格兰杰因果关系检验的方法。研究方法：在混频向量自回归模型（MFVAR）的基础上提出构造Wald统计量,通过模拟实验和实证研究考察统计量的性质。研究发现：模拟实验结果表明该检验相对于其他混频检验和低频检验具有更优的性质,并且对检验式误设具有稳健性。进一步针对中国经济增长与消费者信心因果关系的实证研究证明,混频检验与低频检验得出的结论有很大差异,混频检验得出的结论更符合经济理论。研究创新：利用自助法修正统计量在有限样本下产生的水平扭曲,利用典型相关分析实现了数据降维。研究价值：在检验不同频率变量之间的非线性格兰杰因果关系时避免了信息损失和虚增。     

协整向量、调节参数同为非线性的阈值协整检验

针对经济变量的长期均衡和短期调节关系可能同时存在非线性的事实,本文扩展现有阈值协整模型,提出了协整向量、调节参数都为非线性的阈值协整模型,并着重探讨了该模型的检验方法。研究表明,在协整关系的检验中,Wald统计量有较好的有限样本性质。在协整关系的非线性检验中,LMW和LMG统计量的水平扭曲和检验势都较好。在调节参数的非线性检验中,当调节参数具有显著的非线性时,LMH统计量表现出较好的有限样本性质。     

单位根检验中的Wald统计量研究

本文研究了不同情形下单位根的Wald检验.首先从理论上推导了各种Wald检验统计量的极限分布;然后,运用蒙特卡罗试验,模拟了有限样本容量常用检验水平下的临界值,拟合了临界值关于样本容量的响应面函数,给出了检验统计量的分位数表,并总结了用于单位根检验的Wald统计量有限样本容量下的统计特性.     

非线性误差校正模型中的阈值协整检验——基于阈值协整向量未知的扩展

Kapetanios等(2006)假定阈值协整向量已知,在误差校正模型中使用指数函数刻画非线性调节效应,并使用F懈统计量检验非线性阈值协整.本文基于Kapetanios等(2006)的模型设定,将阈值协整向量由已知扩展为未知,并借鉴Hansen和Seo(2002)的方法估计阈值协整向量和构造F*NEC统计量检验非线性阈值协整.仿真试验表明:本文方法估计的阈值协整向量具有近似无偏、对称的分布和相对较高的精度,并且其随样本容量的变化特征符合一致性.进一步,在有限样本下,F*NEC 与FNEC的水平扭曲没有显著差异,但F*NEC的检验势高于FNEC.     

基于回归模型的列联表独立性检验

本文利用回归模型设计列联表的独立性检验方法。利用虚拟变量技术将列联表定性因素转化为因变量和自变量,构造Wald统计量对二维列联表独立性进行检验,并在此基础上进一步设计方法对高维列联表的独立性问题进行检验。该方法能够将列联表的一些常见的检验问题纳入到一个统一的框架下来进行,有助于人们更好地理解和使用。     

局部平稳性未知条件下STAR模型的线性性检验

本文讨论了局部随机游走STAR模型、局部随机趋势STAR模型的线性性检验问题,构造了Wald类检验统计量,推导出了这些统计量的极限分布,并分析了这些统计量有限样本下的统计特性;本文提出了在局部平稳性未知的条件下,进行STAR模型的线性性检验方法,构建了稳健的检验统计量。检验功效与检验水平分析表明,该统计量具有良好的检验水平及较高的检验功效。     

泛函中心极限定理渐进性与具有GARCH误差项的金融时序单位根检验

本文基于分析泛函中心极限定理在高频金融数据单位根检验中的特征与性质，从随机模拟的角度，探讨了有限样本情况下具有GARCH-GED误差项金融时序的ADF单位根检验统计量乙、乙的统计性质，着重研究了不同水平下的分位数、模型滞后阶的设定及GED分布参数的变动对其检验统计特性的影响。随机模拟结果显示，若数据生成模型设定为AR-GARCH-GED过程，常用的ADF单位根检验统计量存在不同的统计性质，并对出现这种现象的原因进行了探索。     

HAC估计的性质与修正及其在伪回归中的应用研究

本文通过频谱分析揭示了预白化HAC和参数化VARHAC比非参数HAC具有明显优势,并指出传统预白化HAC法由于使用了存在有限样本偏差的OLS法来估计自回归参数,导致其存在有限样本偏差,由此构造的t统计量具有过度拒绝原假设倾向。为了减少预白化HAC的偏差,将OLS估计量的线性修正（LBC）和非线性修正（NBC）嵌入到预白化HAC中,研究表明该法能大大减少长期方差的估计偏差,并通过蒙特卡洛模拟证实对预白化HAC的修正估计能有效减少平稳过程之间的伪回归概率,从而提高了回归模型统计推断的可靠性。     

Higher order approximations for Wald statistics in time series regressions with integrated processes

Asymptotic expansions are developed for Wald test statistics in time series regressions with integrated processes. These expansions provide an opportunity to reduce size distortion in testing by suitable bandwidth selection, and automated rules for doing so are calculated. A band spectral regression and the associated Wald test are also considered. Both the first order and second order properties of the estimator are studied.     

中国宏观经济变量的时间趋势属性研究

本文提出了一种新的时间趋势属性的检验方法,该方法融合了非线性模型与线性模型。本文构建了三个Wald类检验统计量及一个稳健检验统计量,推导出了这些统计量的极限分布并分析了其有限样本下的统计性质。应用该检验程序,本文分析了我国24个重要宏观经济变量的时间趋势属性,结果表明,其中22个经济变量具有非线性平滑转移特征,其时间趋势属性表现为确定性。     

A parametric test of the negativity of the substitution matrix

The negativity of the substitution matrix implies that its latent roots are non-positive. When inequality restrictions are tested, standard test statistics such as a likelihood ratio or a Wald test are not X²-distributed in large samples. We propose a Wald test for testing the negativity of the substitution matrix. The asymptotic distribution of the statistic is a mixture of X²-distributions. The Wald test provides an exact critical value for a given significance level. The problems involved in computing the exact critical value can be avoided by using the upper and lower bound critical values derived by Kodde and Palm (1986). Finally the methods are applied to the empirical results obtained by Barten and Geyskens (1975).     

A Correction for Local Biasedness of the Wald and Null Wald Tests

This paper proposes a procedure to overcome the problem of small-sample local biasedness of the Wald test of a single restriction. The new test procedure involves finding two critical values, in order to obtain the desired size and local unbiasedness. Simulation results indicate that the Wald test corrected in this way still shares the non-monotonic power behaviour of the original test reported in the literature. We extend the new test procedure to the null Wald test recently developed to resolve power non-monotonicity, and obtain good power properties.     

Testing the restrictions implied by the rational expectations hypothesis

The nature and form of the restrictions implied by the rational expectations hypothesis are examined in a variety of models with expectations and the properties of appropriate test statistics are analyzed with Monte Carlo evidence. Specifically, we consider the implications of lagged variables, simultaneous equations, and future period expectations upon the number and functional form of the rational expectations restrictions. Two asymptotically equivalent test statistics — a likelihood ratio and a Wald test — are available for implementing a test of these restrictions. Monte Carlo evidence is offered to provide a comparison between the properties of the alternative test statistics in small samples.     

Stratified studies about risk ratios in 2 × 2 tables with structural zero

Incomplete correlated 2 × 2 tables are common in some infectious disease studies and two‐step treatment studies in which one of the comparative measures of interest is the risk ratio (RR). This paper investigates the two‐stage tests of whether K RRs are homogeneous and whether the common RR equals a freewill constant. On the assumption that K RRs are equal, this paper proposes four asymptotic test statistics: the Wald‐type, the logarithmic‐transformation‐based, the score‐type and the likelihood ratio statistics to test whether the common RR equals a prespecified value. Sample size formulae based on hypothesis testing method and confidence interval method are proposed in the second stage of test. Simulation results show that sample sizes based on the score‐type test and the logarithmic‐transformation‐based test are more accurate to achieve the predesigned power than those based on the Wald‐type test. The score‐type test performs best of the four tests in terms of type I error rate. A real example is used to illustrate the proposed methods.     

Performance of conditional Wald tests in IV regression with weak instruments

We compare the powers of five tests of the coefficient on a single endogenous regressor in instrumental variables regression. Following Moreira [2003, A conditional likelihood ratio test for structural models. Econometrica 71, 1027–1048], all tests are implemented using critical values that depend on a statistic which is sufficient under the null hypothesis for the (unknown) concentration parameter, so these conditional tests are asymptotically valid under weak instrument asymptotics. Four of the tests are based on k-class Wald statistics (two-stage least squares, LIML, Fuller's [Some properties of a modification of the limited information estimator. Econometrica 45, 939–953], and bias-adjusted TSLS); the fifth is Moreira's (2003) conditional likelihood ratio (CLR) test. The heretofore unstudied conditional Wald (CW) tests are found to perform poorly, compared to the CLR test: in many cases, the CW tests have almost no power against a wide range of alternatives. Our analysis is facilitated by a new algorithm, presented here, for the computation of the asymptotic conditional p-value of the CLR test.     

Extension of the Wald statistic to models with dependent observations

A generalization of the Wald statistic for testing composite hypotheses is suggested for dependent data from exponential models which include Lévy processes and diffusion fields. The generalized statistic is proved to be asymptotically chi-squared distributed under regular composite hypotheses. It is simpler and more easily available than the generalized likelihood ratio statistic. Simulations in an example where the latter statistic is available show that the generalized Wald test achieves higher average power than the generalized likelihood ratio test. Received: February 29, 2000     

Inference on transformed stationary time series

The paper is about an approach for parametric inference on instantaneously transformed stationary processes. The paper discusses the asymptotics of the Whittle estimator of the parameters involved and also provides the explicit expression of the asymptotic covariance matrix which does not necessarily require the innovation Gaussianity assumption. As a specific instantaneous transformation, the paper introduces a new version of the Box–Cox transformation and investigates in detail the vector ARMA processes implemented by that transformation, proposing a computation-intensive procedure for parametric estimation and testing. As a computationally feasible test not relying upon the knowledge of the explicit analytic form of the asymptotic covariance matrix or on the information equality, the paper proposes a Monte Carlo Wald test, providing illustrative simulation and real-data examples.