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Asymptotic canonical forms and iterated logarithm rate results of least squares estimates for unstable ARMA models

Asymptotic canonical forms and iterated logarithm rate results of least squares estimates for... Herein we give the asymptotic canonical forms of the design matrixP n =Σ k =1/n X k X′ k whereX′ n =(X(n),...,X(n−p+1)),{X(n)} is an unstable ARMA process Φ(B)X(n)=C(B)ε(n),B denotes the backshift operator such thatB k X(t)=X(t−k), andp is the order of the polynomial Φ(z) having all roots outside or on the unit circle. These asymptotic canonical forms forP n , which behave a.s. approximately diagonally, are then used to obtain the iterated logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Acta Mathematicae Applicatae Sinica Springer Journals

Asymptotic canonical forms and iterated logarithm rate results of least squares estimates for unstable ARMA models

Acta Mathematicae Applicatae Sinica , Volume 12 (3) – Jul 14, 2005

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Publisher
Springer Journals
Copyright
Copyright © 1996 by Science Press, Beijing, China and Allerton Press, Inc., New York, U.S.A.
Subject
Mathematics; Applications of Mathematics; Math Applications in Computer Science; Theoretical, Mathematical and Computational Physics
ISSN
0168-9673
eISSN
1618-3932
DOI
10.1007/BF02011891
Publisher site
See Article on Publisher Site

Abstract

Herein we give the asymptotic canonical forms of the design matrixP n =Σ k =1/n X k X′ k whereX′ n =(X(n),...,X(n−p+1)),{X(n)} is an unstable ARMA process Φ(B)X(n)=C(B)ε(n),B denotes the backshift operator such thatB k X(t)=X(t−k), andp is the order of the polynomial Φ(z) having all roots outside or on the unit circle. These asymptotic canonical forms forP n , which behave a.s. approximately diagonally, are then used to obtain the iterated logarithm rates of almost sure convergence of the least-squares estimates to the unknown true parameter for an unstable time series.

Journal

Acta Mathematicae Applicatae SinicaSpringer Journals

Published: Jul 14, 2005

References