Continuous‐Time Autoregressive Moving Average Processes in Discrete Time: Representation and Embeddability
10 Pages Posted: 24 Aug 2013
Date Written: September 2013
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.
Keywords: Continuous time, ARMA process, discrete‐time representation, embedding
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