On the indirect approaches for CARMA model identification

In this paper, we study the problem of reconstructing a continuous-time (CT) model from an identified discrete-time (DT) model for a continuous-time stochastic process. We present a new necessary and sufficient condition for the existence of the solution. We also show that the solution is unique if it exists. Our results are useful in modeling multivariable processes as well. These results are then used to develop an algorithm where the intermediate discrete-time model estimation is not necessary. The performance of our algorithm is illustrated using numerical simulations.