Pseudo-fractional ARMA modelling using a double Levinson recursion

Abstract

The modelling of fractional linear systems through ARMA models is addressed. To perform this study, a new recursive algorithm for impulse response ARMA modelling is presented. This is a general algorithm that allows the recursive construction of ARMA models from the impulse response sequence. This algorithm does not need an exact order specification, as it gives some insights into the correct orders. It is applied to modelling fractional linear systems described by fractional powers of the backward difference and the bilinear transformations. The analysis of the results leads to propose suitable models for those systems.