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LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE

Published online by Cambridge University Press:  06 December 2006

Zudi Lu  and
Oliver Linton
Zudi Lu
Affiliation:
London School of Economics, Chinese Academy of Sciences, Curtin University of Technology
Oliver Linton
Affiliation:
London School of Economics
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Abstract

Local linear fitting of nonlinear processes under strong (i.e., α-) mixing conditions has been investigated extensively. However, it is often a difficult step to establish the strong mixing of a nonlinear process composed of several parts such as the popular combination of autoregressive moving average (ARMA) and generalized autoregressive conditionally heteroskedastic (GARCH) models. In this paper we develop an asymptotic theory of local linear fitting for near epoch dependent (NED) processes. We establish the pointwise asymptotic normality of the local linear kernel estimators under some restrictions on the amount of dependence. Simulations and application examples illustrate that the proposed approach can work quite well for the medium size of economic time series.We thank Yuichi Kitamura and two referees for helpful comments. This research was partially supported by a Leverhulme Trust research grant, the National Natural Science Foundation of China, and the Economic and Social Science Research Council of the UK.

Type
Research Article
Information
Econometric Theory , Volume 23 , Issue 1 , February 2007 , pp. 37 - 70
Copyright
© 2007 Cambridge University Press

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