In this article we study multivariate continuous-time autoregressive moving-average (MCARMA) processes with values in convex cones. More specifically, introduce matrix-valued MCARMA L\'evy noise and present necessary sufficient conditions for from class to be cone valued. We derive specific hands-on the following two cases: First, classical on $\mathbb{R}_{d}$ positive orthant $\mathbb{R}_{d}^{...

In this note we consider the autoregressive moving average recurrent neural network ARMA-NN(1; 1) process. We show that in contrast to the pure autoregressive process simple ARMA-NN processes exist which are not irreducible. We prove that the controllability of the linear part of the process is sufficient for irreducibility. For the irreducible process essentially the shortcut weight correspond...