A real-time ARMA model structure identification method

The fundamental problem of selecting the order and identifying the time varying parameters of an autoregressive moving average model (ARMA), is one that impacts on many important fields of interest such linear prediction, system identification and spectral analysis. Naturally, it has a long and continuing history and we present an algorithm applicable to on-line/adaptive operation. The method is based on the reformulation of the problem in the standard state space form of the subsequent implementation of a bank of Kalman filters, each fitting a different order model. The problem is reduced then to selecting the true model, using the well known multi-model partitioning theory, for general (not necessarily Gaussian) data PDFs. Furthermore, the method is adaptive, in the sense that it has the ability of tracking successfully changes in the model structure, in real time.