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.