Multi‐Innovation Recursive Methods for a Class of Nonlinear Time Series Models Based on the Penalty Term
Jingyao Niu, Xiao Zhang, Feng Ding, Siyu Liu
Abstract
ABSTRACT This article focuses on the recursive parameter estimation problem of exponential autoregressive (ExpAR) models. Considering the difficulty of the nonlinear optimal problem arising in identifying the ExpAR model, Newton search is used to minimize the criterion function to make the search direction more accurate. A penalty term is incorporated into the criterion function to regularize the parameter updates. To achieve higher accuracy performance under white noise interference, a multi‐innovation Newton recursive algorithm is proposed to make more use of data. To improve the estimation accuracy, a hierarchical two‐stage identification algorithm is adopted. The linear parameters are estimated using recursive least squares, followed by the estimation of the nonlinear parameters through a multi‐innovation Newton recursive algorithm with penalty terms. A simulation example is provided to test the effectiveness of the proposed algorithms.