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本文研究了ADF单位根检验中参数联合约束的拉格朗日乘数检验。首先,本文构建了4个LM统计量并推导了它们的极限分布;然后,运用蒙特卡罗试验,模拟了有限样本容量常用检验水平下的临界值,拟合了临界值关于样本容量的响应面函数,并总结了LM统计量有限样本容量下的统计特性;比较分析了这4个LM统计量的检验功效及实际检验水平;最后,一个实例分析简要说明了这几个统计量在单位根检验中的应用。
Abstract：In this paper we propose Lagrange multiplier tests of joint hypotheses based on the ADF unit root tests.The limiting distributions of the joint LM statistics including the unit root hypothesis are derived,which are functions of Wiener process rather than conventional χ2 distribution.Through Monte Carlo simulations and a response surface functional analysis,we investigate the finite sample distributions of the LM statistics and give the critical values.The power and size of the Lagrange multiplier test are also investigated.Finally,an example is presented to illustrate the Lagrange multiplier statistics for unit root tests.
①见James D.Hamilton,Time Series Analysis,PrincetonUniversity Press,1994,P521-525.
②参见William H.Greene,2002,Econometrics Analysis,第5版495页式(17-45)。此处不直接采用LM检验定义统计量的标准方法,是为了推导极限分布的方便。
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基本信息:
DOI：10.19343/j.cnki.11-1302/c.2010.09.013
中图分类号:O212.1
引用信息:
[1]张凌翔,张晓峒.ADF单位根检验中联合检验LM统计量研究[J].统计研究,2010,27(09):84-90.DOI:10.19343/j.cnki.11-1302/c.2010.09.013.
基金信息:
教育部项目“时间序列非平稳检验理论与应用研究”(项目批准号09YJA79011)的资助
2010-09-15
2010-09-15