Functional-Coefficient Autoregressive Models 论文

摘要

In this paper we study nonparametric estimation and hypothesis testing procedures for the functional coe cient A R ( F AR) models of the form X t = f 1 (X t;d )X t;1 + : : : + f p (X t;d )X t;p + " t , rst 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 successful parametric nonlinear time series models such as the threshold AR models of Tong (1983), exponential AR models of Haggan and Ozaki (1978) and many others.We propose a local linear estimation procedure for estimating the coe cient functions and study its asymptotic properties.In addition, we propose two testing procedures.The rst one tests whether all the coe cient functions are constant (i.e.whether the process is linear).The second one tests if all the coe cient functions are continuous, (i.e. if any threshold type of nonlinearity presents in the process).Some simulation results are presented.