Adaptable Functional Series TARMA Models for Non-Stationary Signal Modelling

Abstract

Functional Series Time-dependent Autoregressive Moving Average (FS-TARMA) models are effective for representing non-stationary random signals arising in a wide variety of applications. Yet, their identification is challenging as, in addition to coefficient of projection estimation, subspace basis function selection is also required. In this study these difficulties are alleviated by postulating adaptive FS-TARMA models, that is models with adaptable basis functions, and a method for their effective identification. This is accomplished via proper basis function parametrizations and a Separable Nonlinear Least Squares (SNLS) type procedure which leads to a reduced dimensionality, constrained, non-quadratic optimization problem tackled via Particle Swarm Optimization (PSO) and gradient-type refinement. The model orders and subspace dimensionalities are also estimated based on PSO optimization and suitable criteria. The method's effectiveness is confirmed via a Monte Carlo study and comparisons with current schemes.