Functional-Coefficient Regression Models for Nonlinear Time Series

Abstract

Functional-co efficient Regression Models for Nonlinear Time Series ZONGWU C A I Department of Mathematics University of North Carolina Charlotte, NC 28223, USA J I A N Q I N G FAN* Department of Statistics University of California Los Angeles, CA 90095, USA QlWEI Yao' Institute of Mathematics and Statistics University of Kent at Canterbury Canterbury, Kent CT2 7NF, U K Abstract We apply the local linear regression technique for estimation of functional-coefficient regres­ sion models for time series data. The models include threshold autoregressive models (Tong 1990) and functional-coefficient autoregressive models (Chen and Tsay 1993) as special cases but with the added advantages such as depicting finer structure of the underlying dynamics and better post-sample forecasting performance. We have also proposed a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined cross-validatory estimation for the expected forecasting errors. The proposed methodology is data-analytic and is of appreciable flexibility to analyze complex and multivariate nonlinear structures without suffering from the curse of dimensionality . The asymptotic properties of the proposed esti­ mators are investigated under the a-mixing condition. Both simulated and real data examples are used for illustration. Keywords: a-mixing; Asymptotic normality; Bootstrap; Forecasting; Goodness-of-fit test; Local linear regression; Nonlinear time series; Varying-coefficient models. *Partially supported by N S F Grant DMS-9803200 and NSA 96-1-0015. +Partially supported by E P S R C Grant L16358 and B B S R C / E P S R C Grant 96/MMI09785.