Pseudolinear estimation of fractionally integrated ARMA (ARFIMA) models with automotive application

Abstract

A novel pseudolinear method for the estimation of fractionally integrated ARMA (ARFIMA) models that are capable of representing combined long- and short-term dependency, is introduced. The method is based on the relationship of the AR/MA parameters and the coefficients of the fractional power operator binomial series expansion with the model's inverse function. These lead to the formulation of a special-form regression problem that can be decomposed into a univariate nonlinear and a multivariate linear regression and may be thus tackled via a special pseudolinear procedure. This decomposition in turn leads to the elimination of the need for initial guess parameter values, drastic simplification in the detection and handling of potential local extrema problems, as well as computational simplicity. The method's strong consistency is established, whereas its performance characteristics are assessed via Monte Carlo experiments and comparisons with the maximum likelihood method. The pseudolinear method is also used for the ARFIMA modeling and prediction of power consumption in an experimental automobile fully active suspension system, the consumption of which is shown to exhibit long-term dependency. A comparison with ARMA/ARIMA type modeling is also made, and the obtained ARFIMA models are shown to achieve improved predictive performance at a drastically reduced parametric complexity.