Abstract
This paper proposes an identification algorithm and a stability criterion for multivariate autoregressive moving average type (ARMA-type) models based on autocorrelation matrices computed from observed sequences of joint input-output processes.
It is firstly shown that the identification of ARMA-type models is closely related to the autoregression of joint input-output processes and both the computational complexity and the memory storage capacity for identifying an ARMA-type model can be reduced by using the fast recursive algorithm, the so-called Levinson-Wiggins-Robinson algorithm for joint input-output processes. Secondly a Lyapunovlike equation is derived, which is associated with more general minimization problems that govern the prediction theory of nonstationary random processes. And by employing this equation the stability of an ARMA-type model with an input white noise is examined.
In this paper the stationarity of joint input-output processes need not be assumed a priori but can be determined through the recursive procedure of the LWR algorithm
