Estimating Semiparametric Arch (Infinity) Models by Kernel Smoothing Methods
77 Pages Posted: 26 Jan 2004
Date Written: August 26, 2003
Abstract
We investigate a class of semiparametric ARCH(infinity) 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 and nonparametric part. We investigate the performance of our procedures on simulated data and on a sample of S&P500 index returns. We find some evidence of asymmetric news impact functions in the daily and weekly data, but some significant differences from the usual shape found in purely parametric analysis.
Keywords: ARCH, Inverse Problem, Kernel Estimation, News Impact Curve, Nonparametric regression, Profile Likelihood, Semiparametric Estimation, Volatility
JEL Classification: C14, G12
Suggested Citation: Suggested Citation
Do you have negative results from your research you’d like to share?
Recommended Papers
-
The Existence and Asymptotic Properties of a Backfitting Projection Algorithm Under Weak Conditions
By Oliver B. Linton, Enno Mammen, ...
-
Estimating Semiparametric Arch (∞) Models by Kernel Smoothing Methods
By Oliver B. Linton and Enno Mammen
-
Yield Curve Estimation by Kernel Smoothing Methods
By Oliver B. Linton, Enno Mammen, ...
-
Yield Curve Estimation by Kernel Smoothing Methods
By Oliver B. Linton, Enno Mammen, ...
-
A Local Instrumental Variable Estimation Method for Generalized Additive Volatility Models
By Woocheol Kim and Oliver B. Linton
-
More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors
By Zhijie Xiao, Oliver B. Linton, ...
-
More Efficient Kernel Estimation in Nonparametric Regression with Autocorrelated Errors
By Raymond Carroll, Oliver B. Linton, ...
-
News - Good or Bad - and its Impact Over Multiple Horizons
By Xilong Chen and Eric Ghysels