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Journal of Financial Econometrics Advance Access originally published online on November 18, 2006
Journal of Financial Econometrics 2007 5(1):1-30; doi:10.1093/jjfinec/nbl007
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Copyright © The Author 2007. Published by Oxford University Press.

Estimating Latent Variables and Jump Diffusion Models Using High-Frequency Data

George J. Jiang and Roel C. A. Oomen
     University of Arizona
     University of Warwick

roel.oomen{at}wbs.ac.uk

roel.oomen{at}wbs.ac.uk


  Abstract

This article proposes a new approach to exploit the information in high-frequency data for the statistical inference of continuous-time affine jump diffusion (AJD) models with latent variables. For this purpose, we construct unbiased estimators of the latent variables and their power functions on the basis of the observed state variables over extended horizons. With the estimates of the latent variables, we propose a generalized method of moments (GMM) procedure for the estimation of AJD models with the distinguishing feature that moments of both observed and latent state variables can be used without resorting to path simulation or discretization of the continuous-time process. Using high frequency return observations of the S&P 500 index, we implement our estimation approach to various continuous-time asset return models with stochastic volatility and random jumps.

KEYWORDS: affine jump diffusion, generalized method of moments, high-frequency data, latent state variables, unbiased minimum-variance estimator

Received March 17, 2006; revised August 18, 2006; accepted September 12, 2006


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