An inner-outer factorization in l<SUP>P</SUP> with applications to ARMA processes

作     者：Cheng, Raymond Ross, William T. 

作者机构：Old Dominion Univ Dept Math & Stat Norfolk VA 23529 USA Univ Richmond Dept Math & Comp Sci Richmond VA 23173 USA 

出 版 物：《JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS》 (数学分析与应用杂志)

年 卷 期：2016年第437卷第1期

页      面：396-418页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

主　　题：Inner-outer factorization Hardy class Time series Autoregressive Moving average Stable process 

摘      要：The following inner-outer type factorization is obtained for the sequence space F: if the complex sequence F = (F-0,F-1, F-2,...) decays geometrically, then for any l(p) sufficiently close to 2 there exist J and G in l(p) such that F = J * G;J is orthogonal in the Birkhoff James sense to all of its forward shifts SJ,S(2)J,S(3)J,...;J and F generate the same S -invariant subspace of F;and G is a cyclic vector for S on l(p). These ideas are used to show that an ARMA equation with characteristic roots inside and outside of the unit circle has Symmetric -a -Stable solutions, in which the process and the given white noise are expressed as causal moving averages of a related i.i.d. SaS white noise. An autoregressive representation of the process is similarly obtained. (C) 2016 Elsevier Inc. All rights reserved.