统计研究
統計研究
통계연구
Statistical Research
2011年
4期
99~105
,共null页
正交多项式逼近 非线性趋势 单位根检验 检验功效
正交多項式逼近 非線性趨勢 單位根檢驗 檢驗功效
정교다항식핍근 비선성추세 단위근검험 검험공효
Orthogonal Polynomial Approximation; Nonlinear Trend; Unit Root Test; Test Power
传统单位根检验方法常常假设带有线性的确定性趋势,但如果趋势是非线性的,通常会因为检验功效大幅下降而导致检验失败。本文研究用正交多项式逼近非线性趋势,然后对残差进行单位根检验的方法,研究了用正交多项式进行趋势逼近的性质,推导了这种方法进行单位根检验时统计量的极限分布,提出了正交多项式最高阶数的确定方法,仿真研究了残差相关与不相关时的检验功效。结果表明,检验方法是有效的。
傳統單位根檢驗方法常常假設帶有線性的確定性趨勢,但如果趨勢是非線性的,通常會因為檢驗功效大幅下降而導緻檢驗失敗。本文研究用正交多項式逼近非線性趨勢,然後對殘差進行單位根檢驗的方法,研究瞭用正交多項式進行趨勢逼近的性質,推導瞭這種方法進行單位根檢驗時統計量的極限分佈,提齣瞭正交多項式最高階數的確定方法,倣真研究瞭殘差相關與不相關時的檢驗功效。結果錶明,檢驗方法是有效的。
전통단위근검험방법상상가설대유선성적학정성추세,단여과추세시비선성적,통상회인위검험공효대폭하강이도치검험실패。본문연구용정교다항식핍근비선성추세,연후대잔차진행단위근검험적방법,연구료용정교다항식진행추세핍근적성질,추도료저충방법진행단위근검험시통계량적겁한분포,제출료정교다항식최고계수적학정방법,방진연구료잔차상관여불상관시적검험공효。결과표명,검험방법시유효적。
Conventional unit root test usually assumes the series has deterministic trend and the trend is linear.But in case of nonlinear trend,the test power becomes impotent drastically,resulting in test failure.Orthogonal polynomial approximation is proposed to estimate deterministic nonlinear trend and then the residual is used to test the unit root.This paper researches the properties of orthogonal polynomial approximation to any linear or nonlinear trend,deduces the limiting distribution of unit root test statistic based on orthogonal polynomial approximation and suggests how to decide the highest order of orthogonal polynomial.The test powers are simulated with residuals correlated or non-correlated.The results show that the proposed method works well.
