Continuous-time autoregressive moving average processes in discrete time: representation and embeddability
Article first published online: 25 APR 2013
Copyright © 2013 Wiley Publishing Ltd.
Journal of Time Series Analysis
Volume 34, Issue 5, pages 552–561, September 2013
How to Cite
Thornton, M. A. and Chambers, M. J. (2013), Continuous-time autoregressive moving average processes in discrete time: representation and embeddability. Journal of Time Series Analysis, 34: 552–561. doi: 10.1111/jtsa.12030
- Issue published online: 23 AUG 2013
- Article first published online: 25 APR 2013
- Manuscript Accepted: 7 MAR 2013
- Manuscript Revised: 29 OCT 2012
- Manuscript Received: 15 JUL 2011
- Continuous time;
- ARMA process;
- discrete-time representation;
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.