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Continuous‐time autoregressive moving average processes in discrete time: representation and embeddability
Author(s) -
Thornton Michael A.,
Chambers Marcus J.
Publication year - 2013
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/jtsa.12030
Subject(s) - autoregressive–moving average model , mathematics , univariate , autoregressive model , discrete time stochastic process , discrete time and continuous time , representation (politics) , moving average , moving average model , stochastic process , autoregressive integrated moving average , statistics , time series , continuous time stochastic process , multivariate statistics , politics , political science , law
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.