Gaussian Processes for Functional-Coefficient Autoregressive Models
نویسنده
چکیده
This work is concerned with nonlinear time series models and, in particular, with nonparametric models for the dynamics of the mean of the time series. We build on the functional-coefficient autoregressive (FAR) model of Chen and Tsay (1993) which is a generalization of the autoregressive (AR) model where the coefficients are varying and are given by functions of the lagged values of the series. We adopt a Bayesian approach for nonparametric functional estimation, modelling the coefficient functions as Gaussain Processes (GPs). We investigate practical implementation issues for our model and describe efficient ways to conduct estimation. We illustrate our proposed method by a study of a simulated and a real data example and we discuss how it can improve over existing estimation techniques for FAR models. Finally, we propose directions for future work which will be aimed, mainly, towards obtaining theoretical results for the procedure, deriving numerical approximation methods for large data sets and assessing the fit of the model.
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