具有GARCH（1，1）-正态误差项的非对称单位根检验研究

摘　　要:理论研究表明许多经济变量呈现出非对称的门限自回归（TAR）或动态门限自回归（M-TAR）数据生成机制,因而非对称单位根检验就成为该领域的主要研究方向之一。本文对非对称单位根检验Enders-Granger方法在GARCH（1,1）-正态误差项下的检验水平与检验势作了系统的仿真研究。研究表明：GARCH（1,1）-正态误差项的TAR或M-TAR模型会对该方法的检验水平和检验势产生重要影响。     

关于ADF与PP单位根检验方法的探讨

经济理论认为许多经济变量具有非对称的阈值自回归调整行为,而标准的单位根检验ADF和PP法都是基于线性自回归模型而构造的,因此对非对称单位根检验并不适用。本文应用Monte-Carlo模拟方法对ADF和PP检验在TAR与M-TAR模型下的检验势进行系统研究,并对模拟结果的产生原因进行了深入分析。模拟结果表明:当非对称程度较大时,ADF和PP的检验势都具有较大幅度的下降,但是ADF比PP法具有更大程度的下降。     

关于ADF与PP单位赧检验方法的探讨

经济理论认为许多经济变量具有非对称的阈值自回归调整行为,而标准的单位根检验ADF和PP法都是基于线性自回归模型而构造的,因此对非对称单位根检验并不适用.本文应用Monte-Cado模拟方法对ADF和PP检验在TAR与M-TAR模型下的检验势进行系统研究,并对模拟结果的产生原因进行了深入分析.模拟结果表明:当非对称程度较大时,ADF和PP的检验势都具有较大幅度的下降,但是ADF比PP法具有更大程度的下降.     

残差块形自助法在非对称单位根检验中的适用性

非对称单位根检验已成为时间序列分析中重要研究领域之一。而当随机干扰项之间具有一般性的自相关时,非对称单位根检验式中,由于不同的滞后阶会对统计量检验势产生至关重要的影响,因此采用残差块形自助法（RBB）对非对称单位根EG检验进行有效的改进研究,并对RBB法的适用性进行了模拟。结果表明：RBB法不仅在一定程度上降低了检验水平扭曲,而且大大提高了EG法的检验势。     

非对称单位根检验和非参数方差比

基于三种退势方法较详细研究了方差比检验在非对称单位根检验中的适用性,并通过MC模拟揭示了其检验势性质。结果表明：在不含趋势项的TAR下,两机制TAR数据落在第一机制的比率是影响方差比检验势的重要因素,且比率越高检验势也越高;三机制TAR中落在中间机制的数据比率会影响检验势,随着比率增加检验势呈下降趋势,但程度不大。在含趋势的TAR下,由于趋势项在数据生成过程中具有支配作用,各种检验势会随着趋势设定的不同而不同。数据在不同机制之间的转换概率越高,则ROLS和RDM退势较OLS退势具有明显优势。     

基于RT-GAS Copula模型的经济金融行业非对称相依性及风险溢出研究

考虑到实体经济行业与金融行业间的相依关系存在杠杆效应，本文采用GJR门限结构将杠杆效应纳入包含高频信息的广义已实现自回归得分Copula(GRAS Copula)模型中，构建广义已实现门限自回归得分Copula(RT-GAS Copula)模型。利用RT-GAS Copula模型揭示实体经济行业与金融行业间时变相依关系对行业收益的非对称响应，并进一步分析经济金融行业间风险溢出的非对称性和时变特征。研究发现：各行业间的相依关系存在显著的杠杆效应，某一行业收益的上涨和下跌对该行业与其他行业间时变相依关系的影响是非对称的；行业间的相依关系会受到国家调控政策和各类市场风险事件的影响；行业间的系统性风险溢出存在非对称性，且会受到严重风险事件的影响。此外，有效性检验结果表明，当行业间相依关系存在显著杠杆效应时，RT-GAS Copula模型的拟合和预测能力优于现有时变Copula模型。     

STAR模型中的递归退势单位根检验研究

在STAR模型框架下,考虑时间序列具有线性确定性趋势成分,本文建立了一个递归退势单位根检验统计量,推导了其渐近分布;并在考虑初始条件情形下,对递归退势、OLS和GLS退势单位根检验统计量的有限样本性质进行了细致的比较研究。若忽略初始条件的影响,GLS退势和递归退势单位根检验统计量的检验势都显著高于OLS退势。随着初始条件的增大,GLS退势单位根检验统计量的检验势下降得比较厉害,递归退势单位根检验统计量的检验势较为稳定,且在样本量较大情形下更具优势。     

分位数单位根检验的有限样本绩效及其应用

利用蒙特卡洛模拟方法,在不同的数据产生过程下比较了分位数单位根检验与传统的ADF和PP单位根检验的绩效。研究发现:当误差项服从正态分布时,传统单位根检验与分位数单位根检验的检验功效相差不大,前者甚至略优于后者;但当误差项服从t分布时,分位数单位根要优于传统的单位根检验。在此基础上,采用中国商品价格指数(增长率)数据,给出分位数单位根检验的实例应用,实证结果显示中国商品价格指数具有非对称的惯性特征。     

利率冲击非对称效应的实证检验:来自中国的经验证据

文章试采用自回归分布滞后(ADL)模型和向量自回归(VAR)模型,对我国利率冲击作用于产出和物价水平效果是否具有非对称性以及非对称的程度、表现形式予以实证研究.计量检验结果表明:正、负向利率冲击对我国宏观经济的影响总体呈现非对称效应;利率冲击时物价的影响,相对于利率冲击对产出的影响而言,其稳定性和持续性更好;利率冲击对物价作用的"非对称效应"强于利率冲击对产出作用的"非对称效应".     

STAR模型中退势单位根检验的小样本性质研究

 Kapetanios et al. (2003)和刘雪燕(2008)提出了ESTAR和LSTAR模型单位根检验的方法。本文将时间序列退势的OLS和GLS方法与他们提出的单位根检验方法结合,通过蒙特卡洛试验发现,在STAR模型中,对时间序列退势能不同程度的改善单位根检验的功效。若时间序列只存在非零均值,ESTAR模型中OLS退势存在优势;LSTAR模型,样本容量较小时（T<=50）,OLS退势的优势较明显,样本容量较大（T>100）时,GLS退势具有了微弱的优势。若序列存在非零的均值和趋势,且样本容量较小时,LSTAR模型中GLS退势的优势较明显,ESTAR模型中OLS退势的优势较明显;样本容量较大时,LSTAR模型中二者功效都很高,ESTAR模型中GLS退势的优势较明显。     

Testing for a unit root in a stationary ESTAR process

This article develops a statistic for testing the null of a linear unit root process against the alternative of a stationary exponential smooth transition autoregressive model. The asymptotic distribution of the test is shown to be nonstandard but nuisance parameter-free and hence critical values are obtained by simulations. Simulations show that the proposed statistic has considerable power under various data generating scenarios. Applications to real exchange rates also illustrate the ability of our test to reject null of unit root when some of the alternative tests do not.     

基于分形理论的LSTAR模型检验

针对非线性时间序列的单位根检验和非线性检验中存在的问题,引入分形理论中的Hurst指数进行研究,以LSTAR模型为代表,讨论了相关样本性质。通过蒙特卡洛模拟实验证实,只有当非平稳特征十分明显时,DF检验才能检测出单位根。Hurst指数改善了单位根检验功效,且作为一种非参数检验方法,具有较好的稳健性。     

Panel data unit roots tests: The role of serial correlation and the time dimension

We investigate the influence of residual serial correlation and of the time dimension on statistical inference for a unit root in dynamic longitudinal data, known as panel data in econometrics. To this end, we introduce two test statistics based on method of moments estimators. The first is based on the generalized method of moments estimators, while the second is based on the instrumental variables estimator. Analytical results for the Instrumental Variables (IV) based test in a simplified setting show that (i) large time dimension panel unit root tests will suffer from serious size distortions in finite samples, even for samples that would normally be considered large in practice, and (ii) negative serial correlation in the error terms of the panel reduces the power of the unit root tests, possibly up to a point where the test becomes biased. However, near the unit root the test is shown to have power against a wide range of alternatives. These findings are confirmed in a more general set-up through a series of Monte Carlo experiments.     

退势单位根检验的小样本性质

在经验研究中,尽管Dickey-Fuller提出的 统计量是应用最广泛的单位根检验,但是,它的检验功效偏低是众所周知的。为了改善Dickey-Fuller检验的功效,本文将时间序列的四种退势方法和 检验、 检验、MAX检验和 检验相结合,通过蒙特卡洛模拟试验研究了16种退势单位根检验的小样本性质。研究发现,退势单位根检验均不同程度地改善了 型检验的功效,特别是退势单位根检验 -KGLS、MAX-KGLS、 -RLS和MAX-RLS具有更理想的小样本性质。     

Unit Root Tests under Time-Varying Variances

The paper provides a general framework for investigating the effects of permanent changes in the variance of the errors of an autoregressive process on unit root tests. Such a framework - which is based on a novel asymptotic theory for integrated and near integrated processes with heteroskedastic errors - allows to evaluate how the variance dynamics affect the size and the power function of unit root tests. Contrary to previous studies, it is shown that non-constant variances can both inflate and deflate the rejection frequency of the commonly used unit root tests, both under the null and under the alternative, with early negative and late positive variance changes having the strongest impact on size and power. It is also shown that shifts smoothed across the sample have smaller impacts than shifts occurring as a single abrupt jump, while periodic variances have a negligible effect even when a small number of cycles take place over a given sample. Finally, it is proved that the locally best invariant (LBI) test of a unit root against level stationarity is robust to heteroskedasticity of any form under the null hypothesis.     

The finite-sample performance of robust unit root tests

This paper investigates the relative small sample performance of several robust unit root tests by means of a simulation study. It is confirmed that the traditional least-squares based Dickey-Fuller test has substantially lower power than several robust alternatives if the error distribution is fat-tailed while its power gain is small at the normal model. Particularly good results are achieved by a quasi-maximum likelihood test. However, all robust tests under consideration exhibit severe size distortions if the disturbances follow a skewed distribution. Moreover, under additive outliers, robust tests fail to produce stable sizes and good power properties. Consequently, the value of using robust unit root tests depends heavily of the type of nonnormality at hand.     

A Nonparametric Test of the Predictive Regression Model

This article considers testing the significance of a regressor with a near unit root in a predictive regression model. The procedures discussed in this article are nonparametric, so one can test the significance of a regressor without specifying a functional form. The results are used to test the null hypothesis that the entire function takes the value of zero. We show that the standardized test has a normal distribution regardless of whether there is a near unit root in the regressor. This is in contrast to tests based on linear regression for this model where tests have a nonstandard limiting distribution that depends on nuisance parameters. Our results have practical implications in testing the significance of a regressor since there is no need to conduct pretests for a unit root in the regressor and the same procedure can be used if the regressor has a unit root or not. A Monte Carlo experiment explores the performance of the test for various levels of persistence of the regressors and for various linear and nonlinear alternatives. The test has superior performance against certain nonlinear alternatives. An application of the test applied to stock returns shows how the test can improve inference about predictability.