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

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  • Nielsen, Mikkel Slot

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.

Suggested Citation

  • Nielsen, Mikkel Slot, 2020. "On non-stationary solutions to MSDDEs: Representations and the cointegration space," Stochastic Processes and their Applications, Elsevier, vol. 130(5), pages 3154-3173.
    • Handle: RePEc:eee:spapps:v:130:y:2020:i:5:p:3154-3173
    DOI: 10.1016/j.spa.2019.09.007
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    References listed on IDEAS

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    1. Runkle, David E, 1987. "Vector Autoregressions and Reality," Journal of Business & Economic Statistics, American Statistical Association, vol. 5(4), pages 437-442, October.
    2. Basse-O’Connor, Andreas & Nielsen, Mikkel Slot & Pedersen, Jan & Rohde, Victor, 2019. "Multivariate stochastic delay differential equations and CAR representations of CARMA processes," Stochastic Processes and their Applications, Elsevier, vol. 129(10), pages 4119-4143.
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