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Functional Coefficient Autoregressive Models: Estimation and Tests of Hypotheses
Author(s) -
Chen Rong,
Liu LonMu
Publication year - 2001
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 - 10.1111/1467-9892.00217
Subject(s) - mathematics , autoregressive model , exponential function , generalization , nonlinear system , parametric statistics , nonparametric statistics , series (stratigraphy) , constant coefficients , linear model , statistics , mathematical analysis , biology , paleontology , physics , quantum mechanics
In this paper, we study nonparametric estimation and hypothesis testing procedures for the functional coefficient AR (FAR) models of the form X t = f 1 ( X t − d ) X t − 1 + ... + f p ( X t − d ) X t − p +ε t , first proposed by Chen and Tsay (1993). As a direct generalization of the linear AR model, the FAR model is a rich class of models that includes many useful parametric nonlinear time series models such as the threshold AR models of Tong (1983) and exponential AR models of Haggan and Ozaki (1981). We propose a local linear estimation procedure for estimating the coefficient functions and study its asymptotic properties. In addition, we propose two testing procedures. The first one tests whether all the coefficient functions are constant, i.e. whether the process is linear. The second one tests if all the coefficient functions are continuous, i.e. if any threshold type of nonlinearity presents in the process. The results of some simulation studies as well as a real example are presented.