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协整关系含非线性时间趋势的向量自回归模型：一致估计AI 解读

This paper studies the consistency of the Gaussian maximum likelihood estimator in a cointegrated vector autoregressive model with nonlinear time trends in cointegrating relations. The results are proved in a coordinate free framework that readily allows for general nonlinear parameter restrictions and makes it possible to show the consistency of reduced form parameter estimators without assuming identifiability of underlying structural parameters. Various consistency…

含结构突变的VAR过程的协整秩检验AI 解读

Tests for the cointegrating rank of a vector autoregressive process are considered that allow for possible exogenous shifts in the mean of the data-generation process. The break points are assumed to be known a priori. It is proposed to estimate and remove the deterministic terms such as mean, linear-trend term, and a shift in a first step. Then systems cointegration tests are applied to the adjusted series. The resulting tests are shown to have known limiting null…

含截距 VAR 过程的协整秩检验AI 解读

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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向量自回归过程中协整向量有效归一化的检验AI 解读

This article develops test procedures for checking the validity of general normalizing restrictions imposed on cointegrating vectors in vector autoregressive processes. Such test procedures are of importance because normalizing restrictions, possibly combined with overidentifying restrictions, are often necessary for a proper interpretation of cointegrating vectors. The null hypothesis of the authors' tests assumes that the employed normalization is valid or, alternatively,…

VAR 过程协整秩似然比检验的局部功效AI 解读

Likelihood ratio (LR) tests for the cointegrating rank of a vector autoregressive process have been developed under different assumptions regarding deterministic terms. For instance, nonzero mean terms and linear trends have been accounted for in some of the tests. In this paper we provide a general framework for deriving the local power properties of these tests. Thereby it is possible to assess the virtue of utilizing varying amounts of prior information by making…

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无限阶协整向量自回归过程AI 解读

Estimation of cointegrated systems via autoregressive approximation is considered in the framework developed by Saikkonen (1992, Econometric Theory 8, 1-27). The asymptotic properties of the estimated coefficients of the autoregressive error correction model (ECM) and the pure vector autoregressive (VAR) representations are derived under the assumption that the autoregressive order goes to infinity with the sample size. These coefficients are often used for analyzing the…

单整与协整系统中极大似然估计渐近理论的困难AI 解读

Problems with the asymptotic theory of nonlinear maximum likelihood estimation in integrated and cointegrated systems are discussed in this paper. One problem is that standard proofs of consistency generally do not apply; another one is that, even if the consistency has been established, it can be difficult to deduce the limiting distribution of a maximum likelihood estimator from a conventional Taylor series expansion of the score vector. It is argued in this paper that the…

ARIMA模型中移动平均单位根的检验AI 解读

Test procedures for detecting overdifferencing or a moving average unit root in Gaussian autoregressive integrated moving average (ARIMA) models are proposed. The tests can be used when an autoregressive unit root is a serious alternative but the hypothesis of primary interest implies stationarity of the observed time series. This is the case, for example, if one wishes to test the null hypothesis that a multivariate time series is cointegrated with a given theoretical…

自回归单位根拉格朗日乘数检验的一则说明AI 解读

It is shown that in a first-order mixed autoregressive moving average model, a Lagrange multiplier test for the autoregressive unit-root hypothesis can be inconsistent against stationary alternatives.

ARIMA 模型差分阶数的点最优检验AI 解读

Deciding the order of differencing is an important part in the specification of an autoregressive integrated moving average (ARIMA) mode. In most, though not all, cases this means deciding whether to use the original observations or their first differences. Common test procedures used in this context are some variants of autoregressive unit root tests. In these tests, one tests the null hypothesis that the order of differencing is one against the alternative that it is zero.…

单整过程的连续弱收敛与随机等度连续性：回归估计应用AI 解读

The concepts of continuous and uniform weak convergence and versions of stochastic equicontinuity are discussed in the context of integrated processes of order one. The considered processes depend on a parameter vector in a specific fashion which is relevant for integrated and cointegrated systems with non-linearities in parameters. The results of the paper can be applied to obtain asymptotic distributions of estimators and test statistics in such systems. In a correctly…

带线性约束的协整向量估计AI 解读

A general approach for the estimation of cointegration vectors with linear restrictions is described. In the special case of zero restrictions, the cointegration relations of the paper are formally similar to the structural form of a traditional simultaneous equation model. The proposed estimation procedures require a conventional rank condition of identification but no exogeneity assumption. In place of exogenous variables there are series that are not cointegrated and can…

通过自回归近似估计与检验协整系统AI 解读

This paper studies the estimation and testing of general cointegrated systems by using an autoregressive approximation. Simple estimators for both the cointegration vectors and their weight matrix in the autoregressive error correction model representation of the system are developed. Since these estimators assume that the number of cointegration vectors and their normalization are fixed in advance, convenient specification tests for checking the validity of these…

协整回归的渐近有效估计AI 解读

An asymptotic optimality theory for the estimation of cointegration regressions is developed in this paper. The theory applies to a reasonably wide class of estimators without making any specific assumptions about the probability distribution or short-run dynamics of the data-generating process. Due to the nonstandard nature of the estimation problem, the conventional minimum variance criterion does not provide a convenient measure of asymptotic efficiency. An alternative…

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