Abstract :
Local linear fitting of nonlinear processes under strong ~i+e+, a-! 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+
