关于单整时间序列非线性变换的研究  

A RECONSIDERATION TO THE NONLINEARTRANSFORMATION OF THE INTEGRATED TIME SERIES

作　　者：张喜彬[1] 张世英[1] 

机构地区：[1]天津大学管理学院

出　　处：《系统工程学报》1998年第2期70-77,共8页Journal of Systems Engineering

基　　金：国家教委博士点专项基金

摘　　要：文献［１］提出了单整序列的非线性变换问题，并对变换序列的统计性质进行了分析．文献［２］也对单整序列的非线性变换问题进行了比较深入的研究，他们都得出结论：一般情况下，一个Ｉ（１）序列的非线性变换会产生一个长期记忆序列，但是变换后的序列未必是一个Ｉ（１）序列．本文讨论了文献［１，２］关于单整序列非线性变换问题的研究方法和基本结论，同时提出了一个新的问题：如果｛Ｘｔ｝和｛Ｙｔ｝都是Ｉ（１）序列，并且它们之间不存在协整关系，那么在什么条件下存在｛Ｘｔ｝和｛Ｙｔ｝的非线性变换，使得变换后的序列是协整的？论文首先根据ＡＣＥ算法，提出了最优非线性变换函数的估计方法，然后对估计后的残差序列进行单位根的检验。Granger and Hallman raise the problem of nonlinear transformations of an integrated process and discuss the statistical properties of the transformed series. Since then several papers are devoted to the studies of nonlinear transformations including Corradi. Both Granger and Hallman and Corradiconclude that nonlinear transformations of an I(1) series generally result in a long memory process,but not necessarily an I(1) process. In this paper we put forward the question that if {Xt} and {Yt} are I(1) and not cointegrated,then whether there exist nonlinear transformations of them such that the transformed series are cointegrated? Based on ACE algorithm, the paper presents the estimating procedure of the nonlinear transformation functions,thus we can proceed the unit root tests on the residual series from the estimated nonlinear transformed series to test for the possible cointegration relationship between the transformed series.

关 键 词：非线性变换 长记忆过程 核平滑 时间序列分析 

分 类 号：O211.61[理学—概率论与数理统计]