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On non-stationary solutions to MSDDEs: representations and the cointegration space

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In this paper we study solutions to multivariate stochastic delay differential equations (MSDDEs) and their relation to the discrete-time cointegrated VAR model. In particular, we observe that an MSDDE can always be written in an error correction form and, under suitable conditions, we argue that a process with stationary increments is a solution to the MSDDE if and only if it admits a certain Granger type representation. A direct implication of these results is a complete characterization of the cointegration space. Finally, the relation between MSDDEs and invertible multivariate CARMA equations is used to introduce the cointegrated MCARMA processes.
Original languageEnglish
JournalStochastic Processes and Their Applications
Number of pages22
ISSN0304-4149
DOIs
Publication statusAccepted/In press - 2019

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