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Nonlinear ARMA models with functional MA coefficients
Author(s) -
Wang HaiBin
Publication year - 2008
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2008.00594.x
Subject(s) - mathematics , autoregressive–moving average model , univariate , nonlinear system , autoregressive model , moment (physics) , parametric model , parametric statistics , moving average model , moving average , function (biology) , statistics , time series , autoregressive integrated moving average , multivariate statistics , physics , classical mechanics , quantum mechanics , evolutionary biology , biology
. In the present article, we propose and study a new class of nonlinear autoregressive moving‐average (ARMA) models, in which each moving‐average (MA) coefficient is enlarged to an arbitrary univariate function. We first provide a sufficient condition for the existence of the stationary solution and further discuss the moment structure. We investigate the estimation method to the proposed models. The global estimates of parameters and local linear estimates of functional coefficients are obtained by using a back‐fitting algorithm. For testing whether the functional coefficients are some specified parametric forms, a bootstrap test approach is provided. The proposed models are illustrated by both simulated and real data examples.