Estimating Semiparametric ARCH(∞) Models by Kernel Smoothing Methods1
Econometrica · 2005 · Volume 73 · Issue 3
DOI: 10.1111/j.1468-0262.2005.00596.x
Abstract
We investigate a class of semiparametric ARCH(∞) models that includes as a special case the partially nonparametric (PNP) model introduced by Engle and Ng (1993) and which allows for both flexible dynamics and flexible function form with regard to the “news impact” function. We show that the functional part of the model satisfies a type II linear integral equation and give simple conditions under which there is a unique solution. We propose an estimation method that is based on kernel smoothing and profiled likelihood. We establish the distribution theory of the parametric components and the pointwise distribution of the nonparametric component of the model. We also discuss efficiency of both the parametric part and the nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find evidence of asymmetric news impact functions, consistent with the parametric analysis.
Keywords
ARCH, inverse problem, kernel estimation, news impact curve, nonparametric regression, profile likelihood, semiparametric estimation, volatility
Enable JavaScript for citation tools and additional paper interactions.