Estimation of the nonlinearity degree for polynomial autoregressive processes with RJMCMC

Abstract

Despite the popularity of linear process models in signal and image processing, various real life phenomena exhibit nonlinear characteristics. Compromising between the realistic and computationally heavy nonlinear models and the simplicity of linear estimation methods, linear in the parameters nonlinear models such as polynomial autoregressive (PAR) models have been accessible analytical tools for modelling such phenomena. In this work, we aim to demonstrate the potentials of Reversible Jump Markov Chain Monte Carlo (RJMCMC) which is a successful statistical tool in model dimension estimation in nonlinear process identification. We explore the capability of RJMCMC in jumping not only between spaces with different dimensions, but also between different classes of models. In particular, we demonstrate the success of RJMCMC in sampling in linear and nonlinear spaces of varying dimensions for the estimation of PAR processes.

Bayesian estimation of polynomial moving average models with unknown degree of nonlinearity

“…In previous studies [7][8][9][10][11], making an assumption that all model subspaces are equally likely a priori, appears as a natural choice in the absence of real prior information about model orders of an observed data. Given these, we assume that the MA order q, and the nonlinearity degree p are uniformly distributed with upper bounds p max and q max :…”

“…In a previous study [11], we demonstrated the success of RJMCMC algorithm in the estimation of PAR processes with unknown degree of nonlinearity. In this study, we reformulate this PAR model estimation problem for the synthetically generated PMA models.…”

“…RJMCMC can also be used for nonlinear model identification problems in a wide range of applications such as a model identification tool for 2016 24th European Signal Processing Conference (EUSIPCO) 978-0-9928-6265-7/16/$31.00 ©2016 IEEE polynomial autoregressive (PAR) models in [11] and threshold moving average (TMA) models in [12].…”

Nonlinear model selection for PARMA processes using RJMCMC

“…In this paper, the formulation in previous studies [22], [23] has been reconstructed into a general framework which estimates the nonlinearity degree of PARMA models. In addition to the nonlinearity degree, AR and MA orders and all the model coefficients have been estimated at the same time.…”

“…In previous studies [22], [23], we have shown that RJMCMC can be used as a model determination method which performs transitions between linear and nonlinear model spaces for polynomial AR (PAR) and polynomial MA (PMA) models.…”