Embedding in law of discrete time ARMA processes in continuous time stationary processes

被引：1
|
作者：
Arratia, Argimiro [1 ]
Cabana, Alejandra [2 ]
Cabana, Enrique M. [3 ]
机构：
[1] Univ Politecn Cataluna, Barcelona, Spain
[2] Univ Autonoma Barcelona, Barcelona, Spain
[3] Univ Republica, Montevideo, Uruguay
来源：
JOURNAL OF STATISTICAL PLANNING AND INFERENCE | 2018年 / 197卷
关键词：
Discrete-time ARMA; Continuous-time ARMA; CARMA; Levy process; Embedding;
D O I：
10.1016/j.jspi.2018.01.004
中图分类号：
O21 [概率论与数理统计]; C8 [统计学];
学科分类号：
020208 ; 070103 ; 0714 ;
摘要：
Given any stationary time series {X-n : n is an element of Z} satisfying an ARMA(p, q) model for arbitrary p and q with infinitely divisible innovations, we construct a continuous time stationary process {chi(t) : t is an element of R} such that the distribution of {chi(n) : n is an element of Z}, the process sampled at discrete time, coincides with the distribution of {X-n}. In particular the autocovariance function of {chi(t)} interpolates that of {X-n }. (C) 2018 Elsevier B.V. All rights reserved.
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页码：156 / 167
页数：12
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