LOCAL LINEAR FITTING UNDER NEAR EPOCH DEPENDENCE

Zudi Lu and Oliver Linton

Econometric Theory, 2007, vol. 23, issue 1, 37-70

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.

Date: 2007
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