  In this paper we study solutions to multivariate stochastic delay
differential equations (MSDDEs) which have stationary increments, and we show
that this modeling framework is in many ways similar 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. As a direct
implication of these results we obtain a complete characterization of the set
of cointegration vectors (the cointegration space). Finally, we exploit the
relation between MSDDEs and invertible multivariate CARMA equations to define
cointegrated MCARMA processes, and we discuss how this definition is related to
earlier literature.
