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

Mikkel Slot Nielsen

Stochastic Processes and their Applications, 2020, vol. 130, issue 5, 3154-3173

Abstract: 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.

Keywords: Cointegration; Error correction form; Granger representation theorem; Multivariate CARMA processes; Multivariate SDDEs; Non-stationary processes (search for similar items in EconPapers)
Date: 2020
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DOI: 10.1016/j.spa.2019.09.007

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