Testing for Cointegration in a System of Equations
方程系统中的协整检验AI 解读 ↓
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方程系统中的协整检验
- 研究问题
- 如何在单方程或多方程系统中，以存在协整为原假设检验非协整，并避免极限分布受到干扰参数影响？
- 方法与思路
- 作者用规范协整回归残差构造多种检验，以向量布朗运动统一表示极限分布，并通过模拟提供部分情形的临界值。
- 材料陈述的贡献
- 摘要称，检验具有一致性；无时间趋势模型中使用完全修正最小二乘残差有相同极限，系统检验在所示模拟中可优于逐方程检验。
- 阅读关注点
- 应核对协整原假设的具体形式、残差修正与趋势处理，以及普通最小二乘残差的问题和多元检验比较的实验条件。
- 阅读边界
- 仅据所给 Crossref 摘要，有限样本优势来自小规模模拟，不能视为普遍结论；完整条件、数值及其他版本变化未说明。
原文摘要
This paper introduces various consistent tests for the null of cointegration against the alternative of noncointegration that can be applied to a system of equations as well as to a single equation. The tests are analogs of Choi and Ahn's (1993, Testing the Null of Stationarity for Multiple Time Series, working paper, The Ohio State University) multivariate tests for the null of stationarity and use Park's (1992, Econometrica 60, 119–143) canonical cointegrating regression (CCR) residuals to make the tests free of nuisance parameters in the limit. The asymptotic distributions of the tests are complex but expressed in unified manner by using standard vector Brownian motion. These distributions are tabulated by simulation for some practical cases. Furthermore, the rates of divergence of the tests are reported. Because there are methods for estimating cointegrating matrices other than CCR, it is illustrated for a model without time trends that the tests we introduce work exactly the same way in the limit when Phillips and Hansen's (1990, Review of Economic Studies 57, 99–125) fully modified ordinary least-squares (OLS) procedure is used. Also, is shown that difficulties arise when OLS residuals are used to formulate the tests. Small-scale simulation results are reported to examine the finite sample performance of the tests. The tests are shown to work reasonably wellin finite samples. In particular, it is illustrated that using the multivariate tests introduced in this paper can be a better testing strategy in terms of the finite sample size and power than applying univariate tests several times to each equation in a system of equations.