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。     

基于参数空间的ST-ECM模型的协整检验问题研究

在非线性平滑转移误差修正模型（ST-ECM）的协整检验中,由于存在未识别参数而使协整检验统计量构造困难,同时由于目前文献普遍使用的泰勒展开近似法并不能精确替代原始非线性模型,从而导致协整检验统计量功效较低。本文首先在遍历未识别参数的参数空间的基础上构造了ST-ECM模型协整检验的supF统计量,推导了supF统计量的极限分布并说明了其收敛性质。接着,蒙特卡洛仿真模拟结果显示,supF统计量在ST-ECM模型协整检验中具有良好的检验水平和功效,且supF统计量的功效明显优于EG统计量、F*NEC统计量和inft统计量。最后,本文对亚洲六个国家的利率期限结构预期假说进行了验证,结果表明中国、新加坡和泰国三个国家的利率期限结构预期假说成立且存在非线性调整效应,supF统计量较其他统计量具有更高的检验功效。     

面板数据非线性阈值协整的检验方法

非线性阈值协整是线性协整的后续发展。本文使用两机制TR模型对Westerlund和Edgerton(2005)的面板数据协整向量结构突变模型进行扩展,提出截距项具有阈值效应、截距项和斜率系数都具有阈值效应的面板数据非线性阈值协整模型。在此基础上,本文进而分别构造Zc、Ztc、Zr、Ztr统计量检验阈值协整,并对上述统计量的极限分布进行了数学推导,发现它们都收敛于随机泛函。仿真实验结果表明,有限样本下上述检验统计量具有较小的水平扭曲和较高的检验势。     

基于结构突变和截面相关的面板协整检验

本文基于Westerlund和Edgerton（2008）,考虑了无时间趋势和有时间趋势的面板协整检验。在检验协整时,本文不仅允许误差项存在异方差、序列相关以及截面相关,而且还允许各截面在截距和协整斜率上存在未知时点的多个突变点。蒙特卡洛模拟结果表明,（1）该检验的具有较小的水平扭曲和较高的检验势,（2）将模型拓展到不含有趋势项的情形是必要的。在此基础上,使用基于动态最小二乘估计量的新统计量对国际CO2排放和经济增长关系进行检验,发现在考虑了突变和截面相关的情形下,两者间的长期均衡关系确实存在。     

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.     

一个时变系数协整回归模型及应用研究

本文通过扩展现有Johansen协整回归模型,允许协整回归模型的系数具有时变特性,并且利用切比雪夫时间多项式来模型化时变系数,提出一个能够捕捉平滑时间转换的时变误差修正模型,并利用极大似然法进行估计。此外,本文还构建了一个用于检验Johansen非时变协整作为原假设的似然比检验,并推断其渐近服从卡方分布。最后应用本文所提出的时变系数协整回归模型检验了人民币汇率购买力平价,结果表明人民币对美元名义汇率、国内消费者价格指数以及美国消费者价格指数之间存在时变协整关系,但系数的符号与理论预期不一致。     

稳健的HAC法在多元平稳时间序列之间伪回归中的应用

本文在传统HAC法的基础上,将截断参数M设定为样本容量T,并推导新的模型显著性检验Wald*统计量的极限分布。通过比较分析,表明Wald*统计量能大大减少伪回归概率,且新统计量比传统检验统计量更加稳健,但是也发现新的统计量具有一定程度的检验水平扭曲,原因在于截断参数M的设定忽略了AR过程的持久性、MA过程的滞后阶等因素,从而导致Wald*存在检验水平扭曲,说明M的设定不当会产生伪回归和检验水平扭曲现象。     

中国金融发展与贸易开放的变结构协整分析

本文运用变结构协整技术分析了我国金融发展与贸易开放之间的长期均衡及短期动态关系.采用循序检验法确定结构突变点,发现在1994年和2003年金融发展与贸易开放之间的协整关系发生突变；对1978～2007年的数据进行变结构协整检验,得到两段变结构关系,并建立了误差修正模型.结果表明,即便是在相关序列存在结构性突变的情况下,...     

基于PVECM的综列协整检验临界值的计算

Groen和Kleibergen(2003)基于综列数据的误差纠正模型(PVECM)和极大似然估计方法,提出了与时间序列中Johanson(1991)协整检验类似的综列协整检验。其似然比检验统计量的极限分布是维纳过程的泛函,所以其临界值需要通过仿真试验来计算,但Groen和Kleibergen(2003)既没有给出具体的临界值也没有给出具体的程序。本文通过对维纳过程的随机积分进行仿真,估计基于PVECM的综列协整检验的临界值。与现有的部分临界值的比较结果显示,我们的计算程序是正确的,计算结果是可靠的。     

Enders-Granger方法在协整检验中的应用研究

本文将协整检验由传统的线性协整检验扩展到线性协整检验和阈值协整检验,并在Enders和Granger(1998)方法的基础上提出了一个新的检验协整是否存在的Sup-F和Sup-F*统计量。通过MC仿真研究发现:在线性协整下,ADF方法比Sup-F法具有更高的检验势,但在"持久性"较强时,Sup-F检验比ADF检验法具有更高的检验势;Sup-F统计量在Three-Regime的阈值协整检验中比ADF法有更高的检验势;Sup-F*在检验协整(包括线性协整和阈值协整)时都具有较低的检验势;随着在不同Regime中自回归系数差距的增大(非对称程度增大),sup-F统计量的检验势提高很快,且比ADF法的检验势高。     

Cointegration in Panel Data with Structural Breaks and Cross‐Section Dependence

The power of standard panel cointegration statistics may be affected by misspecification errors if structural breaks in the parameters generating the process are not considered. In addition, the presence of cross‐section dependence among the panel units can distort the empirical size of the statistics. We therefore design a testing procedure that allows for both structural breaks and cross‐section dependence when testing the null hypothesis of no cointegration. The paper proposes test statistics that can be used when one or both features are present. We illustrate our proposal by analysing the pass‐through of import prices on a sample of European countries. Copyright © 2013 John Wiley & Sons, Ltd.     

Testing cointegration relationship in a semiparametric varying coefficient model

In this paper, we develop two cointegration tests for two varying coefficient cointegration regression models, respectively. Our test statistics are residual based. We derive the asymptotic distributions of test statistics under the null hypothesis of cointegration and show that they are consistent against the alternative hypotheses. We also propose a wild bootstrap procedure companioned with the continuous moving block bootstrap method proposed in  Paparoditis and Politis (2001) and  Phillips (2010) to rectify severe distortions found in simulations when the sample size is small. We apply the proposed test statistic to examine the purchasing power parity (PPP) hypothesis between the US and Canada. In contrast to the existing results from linear cointegration tests, our varying coefficient cointegration test does not reject that PPP holds between the US and Canada.     

Bootstrap testing for the null of no cointegration in a threshold vector error correction model

We develop a test for the linear no cointegration null hypothesis in a threshold vector error correction model. We adopt a sup-Wald type test and derive its null asymptotic distribution. A residual-based bootstrap is proposed, and the first-order consistency of the bootstrap is established. A set of Monte Carlo simulations shows that the bootstrap corrects size distortion of asymptotic distribution in finite samples, and that its power against the threshold cointegration alternative is significantly greater than that of conventional cointegration tests. Our method is illustrated with used car price indexes.     

On the cointegration of international stock indices

This paper investigates the cointegration relationship among a group of international stock indices in light of new developments of econometric methods. Kasa (1992) first documented strong evidence for cointegration relations among five national stock indices, which suggests that there exists a common trend among those stock indices. Using Johansen multivariate cointegration test, we find that his findings are persistent in a sample of longer periods and more countries. In order to investigate whether these results are driven by statistical biases related to the sample size, we apply to our tests the Johansen’s small sample correction factor. The results still point toward the existence of a cointegration relationship but the evidence becomes much weaker. We next examine the empirical patterns emerged from different lag specifications and argue that Kasa’s findings are more likely due to the size distortion in extreme long lag VAR models. Indeed, when we employ a newly developed non-parametric test that does not require estimation VAR models, the null hypothesis of no cointegration cannot be rejected for the original sample of Kasa’s five-country stock indices from 1974 to 1990, nor for the extended period from 1970 to 2003.     

Likelihood based testing for no fractional cointegration

We consider two likelihood ratio tests, the so-called maximum eigenvalue and trace tests, for the null of no cointegration when fractional cointegration is allowed under the alternative, which is a first step to generalize the so-called Johansen’s procedure to the fractional cointegration case. The standard cointegration analysis only considers the assumption that deviations from equilibrium can be integrated of order zero, which is very restrictive in many cases and may imply an important loss of power in the fractional case. We consider the alternative hypotheses with equilibrium deviations that can be mean reverting with order of integration possibly greater than zero. Moreover, the degree of fractional cointegration is not assumed to be known, and the asymptotic null distribution of both tests is found when considering an interval of possible values. The power of the proposed tests under fractional alternatives and size accuracy provided by the asymptotic distribution in finite samples are investigated.     

Multiple Testing for No Cointegration under Nonstationary Volatility

With cointegration tests often being oversized under time‐varying error variance, it is possible, if not likely, to confuse error variance non‐stationarity with cointegration. This paper takes an instrumental variable (IV) approach to establish individual‐unit test statistics for no cointegration that are robust to variance non‐stationarity. The sign of a fitted departure from long‐run equilibrium is used as an instrument when estimating an error‐correction model. The resulting IV‐based test is shown to follow a chi‐square limiting null distribution irrespective of the variance pattern of the data‐generating process. In spite of this, the test proposed here has, unlike previous work relying on instrumental variables, competitive local power against sequences of local alternatives in 1/T‐neighbourhoods of the null. The standard limiting null distribution motivates, using the single‐unit tests in a multiple testing approach for cointegration in multi‐country data sets by combining P‐values from individual units. Simulations suggest good performance of the single‐unit and multiple testing procedures under various plausible designs of cross‐sectional correlation and cross‐unit cointegration in the data. An application to the equilibrium relationship between short‐ and long‐term interest rates illustrates the dramatic differences between results of robust and non‐robust tests.     

Alternative bootstrap procedures for testing cointegration in fractionally integrated processes

This paper considers alternative methods of testing cointegration in fractionally integrated processes, using the bootstrap. The investigation focuses on (a) choice of statistic, (b) use of bias correction techniques, and (c) designing the simulation of the null hypothesis. Three residual-based tests are considered, two of the null hypothesis of non-cointegration, the third of the null hypothesis that cointegration exists. The tests are compared in Monte Carlo experiments to throw light on the relative roles of issues (a)–(c) in test performance.     

A Panel CUSUM Test of the Null of Cointegration*

This paper proposes a simple residual‐based panel CUSUM test of the null hypothesis of cointegration. The test has a limiting normal distribution that is free of nuisance parameters, it is robust to heteroskedasticity and it allows for mixtures of cointegrated and spurious alternatives. Our Monte Carlo results suggest that the test has small‐size distortions and reasonable power. In our empirical application to international R&D spillovers, we present evidence suggesting that total factor productivity is heterogeneously cointegrated with foreign and domestic R&D capital stocks.     

Exact and asymptotic tests for possibly non-regular hypotheses on stochastic volatility models

We study the problem of testing hypotheses on the parameters of one- and two-factor stochastic volatility models (SV), allowing for the possible presence of non-regularities such as singular moment conditions and unidentified parameters, which can lead to non-standard asymptotic distributions. We focus on the development of simulation-based exact procedures–whose level can be controlled in finite samples–as well as on large-sample procedures which remain valid under non-regular conditions. We consider Wald-type, score-type and likelihood-ratio-type tests based on a simple moment estimator, which can be easily simulated. We also propose a C(α)-type test which is very easy to implement and exhibits relatively good size and power properties. Besides usual linear restrictions on the SV model coefficients, the problems studied include testing homoskedasticity against a SV alternative (which involves singular moment conditions under the null hypothesis) and testing the null hypothesis of one factor driving the dynamics of the volatility process against two factors (which raises identification difficulties). Three ways of implementing the tests based on alternative statistics are compared: asymptotic critical values (when available), a local Monte Carlo (or parametric bootstrap) test procedure, and a maximized Monte Carlo (MMC) procedure. The size and power properties of the proposed tests are examined in a simulation experiment. The results indicate that the C(α)-based tests (built upon the simple moment estimator available in closed form) have good size and power properties for regular hypotheses, while Monte Carlo tests are much more reliable than those based on asymptotic critical values. Further, in cases where the parametric bootstrap appears to fail (for example, in the presence of identification problems), the MMC procedure easily controls the level of the tests. Moreover, MMC-based tests exhibit relatively good power performance despite the conservative feature of the procedure. Finally, we present an application to a time series of returns on the Standard and Poor’s Composite Price Index.     

Tests of cointegrating rank with a trend-break

The conventional testing procedure may mislead one into accepting the null of no cointegration or the null of a cointegrating rank smaller than the true rank when there is a trend-break under the alternative hypothesis. This paper proposes tests for cointegrating rank that have power against the trend-break alternative. The proposed tests are applied to the US money demand function. The results support the Campbell–Perron conjecture: money, income and interest rates are cointegrated around a broken trend.