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Functional-Coefficient Regression Models for Nonlinear Time Series
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In this article, the authors apply the local linear regression technique for estimation of functional-efficient regres- sion models for nonlinear time series data and propose a new bootstrap test for the goodness of fit of models and a bandwidth selector based on newly defined crossvalidatory estimation for the expected forecasting errors.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/MMI09785read more
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