Continuous-time autoregressive moving average processes in discrete time: representation and embeddability

被引：8
|
作者：
Thornton, Michael A. [1 ]
Chambers, Marcus J. [2 ]
机构：
[1] Univ York, Heslington YO10 5DD, N Yorkshire, England
[2] Univ Essex, Colchester CO4 3SQ, Essex, England
来源：
JOURNAL OF TIME SERIES ANALYSIS | 2013年 / 34卷 / 05期
基金：
英国经济与社会研究理事会;
关键词：
Continuous time; ARMA process; discrete-time representation; embedding; GAUSSIAN ESTIMATION; DYNAMIC-MODELS; STOCHASTIC TRENDS; ARMA PROCESSES; STATIONARY; PARAMETERS; SYSTEMS;
D O I：
10.1111/jtsa.12030
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This article explores techniques to derive the exact discrete-time representation for data generated by a continuous-time autoregressive moving average (ARMA) process, augmenting existing methods with a stochastic integration-by-parts formula. The continuous-time ARMA(2, 1) system is considered in detail, and a mapping from the parameters of a univariate discrete-time ARMA(2, 1) process to a univariate continuous-time ARMA(2, 1) process observed at discrete intervals is derived. This is used to derive conditions for the embeddability of such processes.
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页码：552 / 561
页数：10
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