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单位根与协整:单位根检验、协整、误差修正与长期关系。
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THE POWER OF SINGLE EQUATION TESTS FOR COINTEGRATION WHEN THE COINTEGRATING VECTOR IS PRESPECIFIED

预先指定协整向量时单方程协整检验的功效

In this paper I present an alternative derivation of the asymptotic distribution of Kremers, Ericsson, and Dolado's (1992, Oxford Bulletin of Economics and Statistics 54, 325–348) conditional error correction model (ECM)–based t -test for cointegration with a single prespecified cointegrating vector. This alternative distribution, which is identical to the distribution of Hansen's (1995, Econometric Theory 11, 1148–1171) covariate augmented t -test for a unit root, is valid…

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TESTING FOR THE COINTEGRATING RANK OF A VAR PROCESS WITH AN INTERCEPT

含截距 VAR 过程的协整秩检验

Testing the cointegrating rank of a vector autoregressive process with an intercept is considered. In addition to the likelihood ratio (LR) tests developed by Johansen and Juselius (1990, Oxford Bulletin of Economics and Statistics , 52, 169–210) and others we also consider an alternative class of tests that is based on estimating the trend parameters of the deterministic term in a different way. The asymptotic local power of these tests is derived and compared to that of…

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Behaviour of the standard and symmetric Dickey-Fuller-type tests when there is a break under the null hypothesis

We examine the behaviour of tests of the unit root null hypothesis when the true generating model is I (1) with a break. Asymptotic distributional results are derived predicting that the standard Dickey–Fuller test will in that case yield frequent rejections of the null for relatively early breaks. This phenomenon is most severe for lowest values of the break fraction under a break in level, and for a break in slope occurring about 15% of the way through the series. However,…

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Confidence Sets for Cointegrating Coefficients Based on Stationarity Tests

基于平稳性检验的协整系数置信集合

Standard methods for inference in cointegrating systems require all the variables to have exact unit roots and are not at all robust even to slight violations of this condition. In this article, I consider an alternative approach to inference in a cointegrating system. This involves testing the hypothesis that a cointegrating vector takes on a specified value by testing for the stationarity of the associated residual. Confidence sets for the cointegrating vector can be…

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ASYMPTOTIC DISTRIBUTIONS FOR UNIT ROOT TEST STATISTICS IN NEARLY INTEGRATED SEASONAL AUTOREGRESSIVE MODELS

近积分季节自回归模型中单位根检验统计量的渐近分布

Seasonal autoregressive models with an intercept or linear trend are discussed. The main focus of this paper is on the models in which the intercept or trend parameters do not depend on the season. One of the most important results from this study is the asymptotic distribution for the ordinary least squares estimator of the autoregressive parameter obtained under nearly integrated condition, and another is the approximation to the limiting distribution of the t -statistic…

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TESTS OF COMMON STOCHASTIC TRENDS

共同随机趋势检验

This paper is concerned with tests in multivariate time series models made up of random walk (with drift) and stationary components. When the stationary component is white noise, a Lagrange multiplier test of the hypothesis that the covariance matrix of the disturbances driving the multivariate random walk is null is shown to be locally best invariant, something that does not automatically follow in the multivariate case. The asymptotic distribution of the test statistic is…

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COINTEGRATION AND DISTANCE BETWEEN INFORMATION SETS

协整与信息集之间的距离

This paper investigates Granger noncausality and the cointegrating relation between two time series in the Hilbert space framework. This framework allows us to analyze the relationship between cointegration and distance between two information sets. In particular, we prove that if two variables, X and Y , are cointegrated, then the distance between two information sets, concerning the differenced series Δ X and Δ Y , must be less than the standard deviation of Δ X .

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Estimating Restricted Cointegrating Vectors

受限协整向量的估计

This article suggests the use of simple minimum-distance methods to estimate restricted cointegrating vectors. The method directly employs minimum-distance methods on unrestricted cointegrating matrices estimated in the usual way to estimate restricted parameters that are linearly or nonlinearly related to the unrestricted cointegrating vector coefficients. The limiting distribution of the estimates and the usual test for the restrictions are derived. A Monte Carlo…

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Residual-Based Tests for Normality in Autoregressions: Asymptotic Theory and Simulation Evidence

自回归模型中基于残差的正态性检验:渐近理论与模拟证据

Existing results for the asymptotic validity of the Jarque-Bera test in vector autoregressive (VAR) models assume stationarity. In applied work, however, researchers often work with possibly integrated and cointegrated process. We prove the asymptotic validity of the Jarque-Bera test for vector error-correction (VEC) models and for unrestricted VAR models with possibly integrated or cointegrated variables. We also propose the use of bootstrap critical values in stationary…

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Strongly Consistent Determination of Cointegrating Rank Via Canonical Correlations

基于典型相关的协整秩强一致判定

This article is concerned with the statistical analysis of nonstationary, cointegrated time series. The estimation of the cointegrating structure of such time series is considered, and the problem of identifying the cointegrating rank is addressed. A methodology is presented that leads to strongly consistent estimates of this quantity. The identification is based on a canonical correlation analysis of the original variables and presents an alternative approach to those…

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US deficit sustainability: a new approach based on multiple endogenous breaks

美国赤字的可持续性:基于多个内生断点的新方法

Recent empirical work has questioned the consistency of US fiscal policy with an intertemporal budget constraint. Empirical results have tended to indicate that the deficit process has undergone at least one structural shift during recent decades, with the deficit becoming either unsustainable or sustainable in only a weak sense in the post-shift period. In this paper, we re-examine sustainability using a new approach, based on a cointegration model with multiple endogenous…

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Some tests for parameter constancy in cointegrated VAR‐models

协整VAR模型中的若干参数稳定性检验

Some methods for the evaluation of parameter constancy in cointegrated vector autoregressive (VAR) models are discussed. Two different ways of re-estimating the VAR-model are proposed; one in which all parameters are estimated recursively based upon the likelihood function for the first observations, and another in which the cointegrating relations are estimated recursively from a likelihood function, where the short-run parameters have been concentrated out. We suggest…

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APPROXIMATION OF THE ASYMPTOTIC DISTRIBUTION OF THE LOG LIKELIHOOD RATIO TEST FOR COINTEGRATION

协整对数似然比检验渐近分布的近似

Tail approximation of the asymptotic distribution of the log likelihood ratio test for cointegration in a vector autoregressive process is studied. In dimension 2, an approximation of weighted χ 2 type is derived by applying multivariate saddlepoint approximation techniques to a Fourier inversion integral.

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Estimation When a Parameter is on a Boundary

参数位于边界时的估计

This paper establishes the asymptotic distribution of extremum estimators when the true parameter lies on the boundary of the parameter space. The boundary may be linear, curved, and/or kinked. Typically the asymptotic distribution is a function of a multivariate normal distribution in models without stochastic trends and a function of a multivariate Brownian motion in models with stochastic trends. The results apply to a wide variety of estimators and models. Examples…

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Adaptive estimation of cointegrated models: simulation evidence and an application to the forward exchange market

协整模型的自适应估计:模拟证据与远期外汇市场应用

The paper reports simulation and empirical evidence on the finite-sample performance of adaptive estimators in cointegrated systems. Adaptive estimators are asymptotically efficient, even when the shape of the likelihood function is unknown. We consider two representations of cointegrated systems--triangular cointegrating regressions and error correction models. The motivation for and advantages of adaptive estimators in such systems are discussed and their construction is…

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Bayesian Unit-Root Testing in Stochastic Volatility Models

随机波动率模型中的贝叶斯单位根检验

This article uses a Bayesian unit-root test in stochastic volatility models. The time series of interest is the volatility that is unobservable. The unit-root testing is based on the posterior odds ratio, which is approximated by Markov-chain Monte Carlo methods. Simulations show that the testing procedure is efficient for moderate sample size. The unit-root hypothesis is rejected in seven market indexes, and some evidence of nonstationarity is observed in the TWSI of Taiwan.

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COINTEGRATING REGRESSIONS WITH TIME VARYING COEFFICIENTS

具有时变系数的协整回归

This paper considers cointegrating regressions with time varying coefficients. The coefficients are modeled as smooth functions evolving over time. It is shown that they can be estimated nonparametrically, using suitably modified series estimators. Presented is the efficient method of estimation, which relies on simple prefiltering of the data and preestimation of the model. The test for the adequacy of model specification is also developed. Our model and statistical methods…

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Linear Regression Limit Theory for Nonstationary Panel Data

非平稳面板数据的线性回归极限理论

This paper develops a regression limit theory for nonstationary panel data with large numbers of cross section and time series observations. The limit theory allows for both sequential limits and joins limits, and the relationship between these multidimensional limits is explored. The panel structures considered allow for no time series cointegration, heterogeneous cointegration, homogeneous cointegration, and near-homogeneous cointegration. The paper explores the existence…

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Numerical distribution functions of likelihood ratio tests for cointegration

协整似然比检验的数值分布函数

This paper employs response surface regressions based on simulation experiments to calculate asymptotic distribution functions for the Johansen-type likelihood ratio tests for cointegration. These are carried out in the context of the models recently proposed by Pesaran, Shin, and Smith (1997) that allow for the possibility of exogenous variables integrated of order one. The paper calculates critical values that are very much more accurate than those available previously.…

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