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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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ESTIMATION OF UNIT ROOT SPATIAL DYNAMIC PANEL DATA MODELS

单位根空间动态面板数据模型的估计

This paper examines the asymptotics of the QMLE for unit root dynamic panel data models with spatial effect and fixed effects. We consider a unit root dynamic panel data model with spatially correlated disturbances and a unit root spatial dynamic panel data model. For both models the estimate of the dynamic coefficient is $\root \of {nT^3 }$ consistent and the estimates of other parameters are $\root \of {nT}$ consistent, and all of them are asymptotically normal. For the…

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UNIT ROOT TESTS WITH WAVELETS

基于小波的单位根检验

This paper develops a wavelet (spectral) approach to testing the presence of a unit root in a stochastic process. The wavelet approach is appealing, since it is based directly on the different behavior of the spectra of a unit root process and that of a short memory stationary process. By decomposing the variance (energy) of the underlying process into the variance of its low frequency components and that of its high frequency components via the discrete wavelet…

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Some thoughts on the development of cointegration

关于协整发展的若干思考

This paper describes how the notion of cointegration came about, and discusses some generalizations to indicate where the topic may go next. In particular, some issues in the analysis of possibly cointegrated quantile time series are discussed.

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Averaging estimators for autoregressions with a near unit root

近单位根自回归模型的平均估计量

This paper uses local-to-unity theory to evaluate the asymptotic mean-squared error (AMSE) and forecast expected squared error from least-squares estimation of an autoregressive model with a root close to unity. We investigate unconstrained estimation, estimation imposing the unit root constraint, pre-test estimation, model selection estimation, and model average estimation. We find that the asymptotic risk depends only on the local-to-unity parameter, facilitating simple…

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Speed of adjustment in cointegrated systems

协整系统的调整速度

This paper discusses summary measures for the speed of adjustment in possibly cointegrated Vector Autoregressive Processes (VAR). In particular we propose long-run half-lives, based on interim and total multipliers. We discuss their relation with Granger-noncausality and other types of half-life, which are shown to convey different information, except in the univariate AR(1) case. We present likelihood-based inference on long-run half-lives, regarded as discrete functions of…

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Cointegration, long-run structural modelling and weak exogeneity: Two models of the UK economy

协整、长期结构建模与弱外生性:两个英国经济模型

Cointegration ideas as introduced by Granger in 1981 are commonly embodied in empirical macroeconomic modelling through the vector error correction model (VECM). It has become common practice in these models to treat some variables as weakly exogenous, resulting in conditional VECMs. This paper studies the consequences of different approaches to weak exogeneity for the dynamic properties of such models, in the context of two models of the UK economy, one a national-economy…

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Likelihood based testing for no fractional cointegration

无分数协整的似然检验

We consider two likelihood ratio tests, 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…

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Cointegration in a historical perspective

历史视角下的协整

We analyse the impact of the Engle and Granger (1987) article by means of its citations over time, and find evidence of a second life starting in the new millennium. Next, we propose a possible explanation of the success of this citation classic. We argue that the conditions for its success were just right at the time of its appearance, because of the growing emphasis on time series properties in econometric modelling, the empirical importance of stochastic trends, the…

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Likelihood-based inference for cointegration with nonlinear error-correction

非线性误差修正协整模型的似然推断

We consider a class of nonlinear vector error correction models where the transfer function (or loadings) of the stationary relationships is nonlinear. This includes in particular the smooth transition models. A general representation theorem is given which establishes the dynamic properties of the process in terms of stochastic and deterministic trends as well as stationary components. In particular, the behavior of the cointegrating relations is described in terms of…

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Model-based asymptotic inference on the effect of infrequent large shocks on cointegrated variables

低频大冲击对协整变量影响的模型化渐近推断

Quasi-maximum-likelihood (QML) estimation of a model combining cointegration in the conditional mean and rare large shocks (outliers) with a factor structure in the innovations is studied. The goal is not only to robustify inference on the conditional-mean parameters, but also to find regularities and conduct inference on the instantaneous and long-run effect of the large shocks. Given the cointegration rank and the factor order, [chi]2 asymptotic inference is obtained for…

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Testing for co-integration in vector autoregressions with non-stationary volatility

非平稳波动率向量自回归中的协整检验

Many key macroeconomic and financial variables are characterized by permanent changes in unconditional volatility. In this paper we analyse vector autoregressions with non-stationary (unconditional) volatility of a very general form, which includes single and multiple volatility breaks as special cases. We show that the conventional rank statistics computed as in (Johansen, 1988) and (Johansen, 1991) are potentially unreliable. In particular, their large sample distributions…

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Forecasting with equilibrium-correction models during structural breaks

结构突变期间均衡修正模型的预测

When location shifts occur, cointegration-based equilibrium-correction models (EqCMs) face forecasting problems. We consider alleviating such forecast failure by updating, intercept corrections, differencing, and estimating the future progress of an 'internal' break. Updating leads to a loss of cointegration when an EqCM suffers an equilibrium-mean shift, but helps when collinearities are changed by an 'external' break with the EqCM staying constant. Both mechanistic…

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Semiparametric inference in multivariate fractionally cointegrated systems

多变量分数协整系统的半参数推断

A semiparametric multivariate fractionally cointegrated system is considered, integration orders possibly being unknown and I(0) unobservable inputs having nonparametric spectral density. Two estimates of the vector of cointegrating parameters [nu] are considered. One involves inverse spectral weighting and the other is unweighted but uses a spectral estimate at frequency zero. Both corresponding Wald statistics for testing linear restrictions on [nu] are shown to have a…

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Robust methods for detecting multiple level breaks in autocorrelated time series

自相关时间序列中多个水平突变的稳健检测

In this paper we propose tests for the null hypothesis that a time series process displays a constant level against the alternative that it displays (possibly) multiple changes in level. Our proposed tests are based on functions of appropriately standardized sequences of the differences between sub-sample mean estimates from the series under investigation. The tests we propose differ notably from extant tests for level breaks in the literature in that they are designed to be…

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IMPROVED AND EXTENDED END-OF-SAMPLE INSTABILITY TESTS USING A FEASIBLE QUASI-GENERALIZED LEAST SQUARES PROCEDURE

利用可行准广义最小二乘改进和扩展样本末端不稳定性检验

This paper extends the Andrews (2002, Econometrica 71, 1661–1694) and Andrews and Kim (2006, Journal of Business & Economic Statistics 24, 379–394) ordinary least squares–based end-of-sample instability tests for linear regression models. The author proposes to quasi-difference the data first using a consistent estimate of the sum of the autoregressive coefficients of the error process and then test for the end-of-sample instability. For the cointegration model, the feasible…

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PANEL UNIT ROOT TESTS WITH CROSS-SECTION DEPENDENCE: A FURTHER INVESTIGATION

存在截面依赖的面板单位根检验:进一步研究

An effective way to control for cross-section correlation when conducting a panel unit root test is to remove the common factors from the data. However, there remain many ways to use the defactored residuals to construct a test. In this paper, we use the panel analysis of nonstationarity in idiosyncratic and common components (PANIC) residuals to form two new tests. One estimates the pooled autoregressive coefficient, and one simply uses a sample moment. We establish their…

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Long‐run relations in European electricity prices

欧洲电力价格的长期关系

Abstract This paper analyses the interdependencies existing in wholesale electricity prices in six major European countries. The results of a robust multivariate long‐run dynamic analysis reveal the presence of four highly integrated central European markets (France, Germany, the Netherlands and Austria). The trend shared by these four electricity markets appears to be common also to gas prices, but not to oil prices. The existence of a common long‐term dynamics among…

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A generalized nonlinear IV unit root test for panel data with cross-sectional dependence

允许截面依赖的面板数据广义非线性工具变量单位根检验

This paper proposes a unit root test for panel data with cross-sectional dependence. The test generalizes the nonlinear IV unit root test of Chang (2002) to the case where there exist some common factors in panels. The main idea is to eliminate the cross-sectional dependence through the method of principal components as in Bai and Ng (2004) and then apply Chang's test to the treated data. Under certain conditions, the proposed test is consistent and has a standard normal…

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A semiparametric cointegrating regression: Investigating the effects of age distributions on consumption and saving

半参数协整回归:年龄分布对消费与储蓄的影响

We consider a semiparametric cointegrating regression model, for which the disequilibrium error is further explained nonparametrically by a functional of distributions changing over time. The paper develops the statistical theories of the model. We propose an efficient econometric estimator and obtain its asymptotic distribution. A specification test for the model is also investigated. The model and methodology are applied to analyze how an aging population in the US…

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A SIEVE BOOTSTRAP TEST FOR COINTEGRATION IN A CONDITIONAL ERROR CORRECTION MODEL

条件误差修正模型中的协整筛式 bootstrap 检验

In this paper we propose a bootstrap version of the Wald test for cointegration in a single-equation conditional error correction model. The multivariate sieve bootstrap is used to deal with dependence in the series. We show that the introduced bootstrap test is asymptotically valid. We also analyze the small sample properties of our test by simulation and compare it with the asymptotic test and several alternative bootstrap tests. The bootstrap test offers significant…

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ANALYSIS OF COEXPLOSIVE PROCESSES

共爆炸过程分析

A vector autoregressive model allowing for unit roots as well as an explosive characteristic root is developed. The Granger-Johansen representation shows that this results in processes with two common features: a random walk and an explosively growing process. Cointegrating and coexplosive vectors can be found that eliminate these common factors. The likelihood ratio test for a simple hypothesis on the coexplosive vectors is analyzed. The method is illustrated using data…

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TESTS FOR NONLINEAR COINTEGRATION

非线性协整检验

This paper develops tests for the null hypothesis of cointegration in the nonlinear regression model with I (1) variables. The test statistics we use in this paper are Kwiatkowski, Phillips, Schmidt, and Shin’s (1992; KPSS hereafter) tests for the null of stationarity, though using other kinds of tests is also possible. The tests are shown to depend on the limiting distributions of the estimators and parameters of the nonlinear model when they use full-sample residuals from…

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Nonparametric cointegration analysis of fractional systems with unknown integration orders

未知单整阶数的分数系统非参数协整分析

In this paper a nonparametric variance ratio testing approach is proposed for determining the cointegration rank in fractionally integrated systems. The test statistic is easily calculated without prior knowledge of the integration order of the data, the strength of the cointegrating relations, or the cointegration vector(s). The latter property makes it easier to implement than regression-based approaches, especially when examining relationships between several variables…

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Weighted least squares approximate restricted likelihood estimation for vector autoregressive processes

向量自回归过程的加权最小二乘近似限制似然估计

We derive a weighted least squares approximate restricted likelihood estimator for a k-dimensional pth-order autoregressive model with intercept. Exact likelihood optimization of this model is generally infeasible due to the parameter space, which is complicated and high-dimensional, involving pk2 parameters. The weighted least squares estimator has significantly reduced bias and mean squared error than the ordinary least squares estimator for both stationary and…

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