Fitting the exponential autoregressive model through recursive search

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This paper focuses on the recursive parameter estimation methods for the exponential autoregressive (ExpAR) model. Applying the negative gradient search and introducing a forgetting factor, a stochastic gradient and a forgetting factor stochastic gradient algorithms are presented. In order to improve the parameter estimation accuracy and the convergence rate, the multi-innovation identification theory is employed to derive a forgetting factor multi-innovation stochastic gradient algorithm. A simulation example is provided to test the effectiveness of the proposed algorithms.