THE LIVE METHOD FOR GENERALIZED ADDITIVE VOLATILITY MODELS

Abstract

We investigate a new separable nonparametric model for time series, which includes many autoregressive conditional heteroskedastic (ARCH) models and autoregressive (AR) models already discussed in the literature. We also propose a new estimation procedure called LIVE, or local instrumental variable estimation, that is based on a localization of the classical instrumental variable method. Our method has considerable computational advantages over the competing marginal integration or projection method. We also consider a more efficient two-step likelihood-based procedure and show that this yields both asymptotic and finite-sample performance gains.This paper is based on Chapter 2 of the first author's Ph.D. dissertation from Yale University. We thank Wolfgang Härdle, Joel Horowitz, Peter Phillips, and Dag Tjøstheim for helpful discussions. We are also grateful to Donald Andrews and two anonymous referees for valuable comments. The second author thanks the National Science Foundation and the ESRC for financial support.