Estimating Semiparametric Arch (Infinity) Models by Kernel Smoothing Methods

77 Pages Posted: 26 Jan 2004

See all articles by Enno Mammen

Enno Mammen

University of Mannheim - Department of Economics

Oliver B. Linton

University of Cambridge

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

Mammen, Enno and Linton, Oliver B., Estimating Semiparametric Arch (Infinity) Models by Kernel Smoothing Methods (August 26, 2003). Available at SSRN: https://ssrn.com/abstract=489342 or http://dx.doi.org/10.2139/ssrn.489342

Enno Mammen

University of Mannheim - Department of Economics ( email )

Mannheim, 68131
Germany

Oliver B. Linton (Contact Author)

University of Cambridge ( email )

Faculty of Economics
Cambridge, CB3 9DD
United Kingdom