Pseudo-Fractional ARMA modelling using a double Levinson recursion

1 UNINOVA and DEE, Faculdade de Ciências e Tecnologia da Universidade Nova de Lisboa, Campus da FCT da UNL, Quinta da Torre, 2829-516 Caparica, Portugal 2 INESC ID, Rua Alves Redol, 9, 2o, 1000-029 Lisboa, Portugal 3 L2F INESC ID, Rua Alves Redol, 9, 2o, 1000-029 Lisboa, Portugal 4 Academia Militar, Rua Gomes Freire, 1150-175 Lisboa, Portugal Abstract – In this paper the modeling 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, since 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 us to propose suitable models for those systems.