Generalized Method of Integrated Moments for High-Frequency Data

Abstract

We propose a semiparametric two-step inference procedure for a finite-dimensional parameter based on moment conditions constructed from high-frequency data. The population moment conditions take the form of temporally integrated functionals of state-variable processes that include the latent stochastic volatility process of an asset. In the first step, we nonparametrically recover the volatility path from high-frequency asset returns. The nonparametric volatility estimator is then used to form sample moment functions in the second-step GMM estimation, which requires the correction of a high-order nonlinearity bias from the first step. We show that the proposed estimator is consistent and asymptotically mixed Gaussian and propose a consistent estimator for the conditional asymptotic variance. We also construct a Bierens-type consistent specification test. These infill asymptotic results are based on a novel empirical-process-type theory for general integrated functionals of noisy semimartingale processes.

Keywords: high frequency data, semimartingale, spot volatility, nonlinearity bias, GMM