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Continuous Time ARMA processes in Discrete Time: Representation and Embeddability

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Publication details

JournalJournal of Time Series Analysis
DateE-pub ahead of print - 25 Apr 2013
DatePublished (current) - Sep 2013
Issue number5
Volume34
Number of pages9
Pages (from-to)552-561
Early online date25/04/13
Original languageEnglish

Abstract

This paper explores techniques to derive the exact discrete time representation for data generated by a continuous time ARMA (autoregressive moving average) process, deploying Bergstrom's (1983) widely used method, augmented by 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.

    Research areas

  • Continuous time, ARMA process, discrete time representation, embedding

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