Analyzing Relationships between Ctarma and Arma Models

A linear Markov system can be represented by an autoregressive and moving average (ARMA) model in discrete time domain. It can be used to identify some system model and its associated parameters. Recently, the ARMA model has been extended to an ARMA-LiNGAM model which is a canonical form to represent the system. It is expected to provide more detailed information of the model structure and the parameters. In this paper, we extend the model to a more generic ARMA-LiNGM model and analyze the relationships between the ARMALiNGM model and a CTARMA model which is another canonical form of the system model in continuous time domain. As the consequence, we provide the relations between the coefficients of the two models, which can help us to overcome limitations of a classical ARMA model on the identification of the model and its parameters.