LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE

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+