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参数已知的潜在协整向量非平稳性检验的最优功效AI 解读

Theory often specifies a particular cointegrating vector among integrated variables, and testing for a unit root in the known cointegrating vector is often required. Although it is common to simply use a univariate test for a unit root for this test, it is known that this does not take into account all available information. We show here that in such testing situations, a family of tests with optimality properties exists. We use this to characterize the extent of the loss in…

Unbiasedness of the OLS estimator with random regressors—solution.

A new class of autocorrelation robust test statistics is introduced. The class of tests generalizes the Kiefer, Vogelsang, and Bunzel (2000) test in a manner analogous to Anderson and Darling's (1952) generalization of the Cramér–von Mises goodness of fit test. In a Gaussian location model, the error in rejection probability of the new tests is found to be O(T-1logT), where T denotes the sample size.

利用协变量的平稳性检验AI 解读

Two new stationarity tests are proposed. Both tests can be viewed as generalizations of existing stationarity tests and dominate these in terms of local asymptotic power. Improvements are achieved by accommodating stationary covariates. A Monte Carlo investigation of the small sample properties of the tests is conducted, and an empirical illustration from international finance is provided.This paper has benefited from the comments of Pentti Saikkonen (the co-editor), two…

Unbiasedness of the OLS estimator with random regressors.

利用平稳协变量进行单位根检验AI 解读

We derive the family of tests for a unit root with maximal power against a point alternative when an arbitrary number of stationary covariates are modeled with the potentially integrated series. We show that very large power gains are available when such covariates are available. We then derive tests which are simple to construct (involving the running of vector autoregressions) and achieve at a point the power envelopes derived under very general conditions. These tests…

线性过程的协方差矩阵一致估计AI 解读

Consistency of kernel estimators of the long-run covariance matrix of a linear process is established under weak moment and memory conditions. In addition, it is pointed out that some existing consistency proofs are in error as they stand.

近协整时间序列的回归理论AI 解读

This paper proposes a notion of near cointegration and generalizes several existing results from the cointegration literature to the case of near cointegration. In particular, the properties of conventional cointegration methods under near cointegration are characterized, thereby investigating the robustness of cointegration methods. In addition, we obtain local asymptotic power functions of five cointegration tests that take cointegration as the null hypothesis.