Modeling a nonlinear process using the exponential autoregressive time series model

Xu, Huan and Ding, Feng and Yang, Erfu (2019) Modeling a nonlinear process using the exponential autoregressive time series model. Nonlinear Dynamics, 95 (3). pp. 2079-2092. ISSN 0924-090X (https://doi.org/10.1007/s11071-018-4677-0)

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Abstract

The parameter estimation methods for the nonlinear exponential autoregressive (ExpAR) model are investigated in this work. Combining the hierarchical identification principle with the negative gradient search, we derive a hierarchical stochastic gradient algorithm. Inspired by the multi-innovation identification theory, we develop a hierarchical-based multi-innovation identification algorithm for the ExpAR model. Introducing two forgetting factors, a variant of the hierarchical-based multi-innovation identification algorithm is proposed. Moreover, to compare and demonstrate the serviceability of these algorithms, a nonlinear ExpAR process is taken as an example in the simulation.

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