Generalized Methods of Integrated Moments for High-Frequency Data

Abstract

We study the asymptotic inference for a conditional moment equality model using highfrequency data sampled within a fixed time span. The model involves the latent spot variance of an asset as a covariate. We propose a two-step semiparametric inference procedure by first nonparametrically recovering the volatility path from asset returns and then conducting inference by matching integrated moment conditions. We show that, due to the first-step estimation error, a bias-correction is needed for the sample moment condition to achieve asymptotic (mixed) normality. We provide feasible inference procedures for the model parameter and establish their asymptotic validity. Empirical applications on VIX pricing and the volatility-volume relationship are provided to illustrate the use of the proposed method.