Just as ARMA processes play a central role in the representation of stationary time series with discrete time parameter, <InlineEquation ID="IEq1"> <EquationSource Format="TEX">$$(Y_n)_{n\in \mathbb {Z}}$$</EquationSource> <EquationSource Format="MATHML"> <math xmlns:xlink="http://www.w3.org/1999/xlink"> <msub> <mrow> <mo stretchy="false">(</mo> <msub> <mi>Y</mi> <mi>n</mi> </msub> <mo stretchy="false">)</mo> </mrow> <mrow> <mi>n</mi> <mo>∈</mo> <mi mathvariant="double-struck">Z</mi> </mrow> </msub> </math> </EquationSource> </InlineEquation>, CARMA processes play an analogous role in the representation of stationary time series with continuous time...</equationsource></equationsource></inlineequation>

We consider the parametric estimation of the driving Lévy process of a multivariate continuous-time autoregressive moving average (MCARMA) process, which is observed on the discrete time grid (0,h,2h,…). Beginning with a new state space representation, we develop a method to recover the...