Estimating Latent Variables and Jump Diffusion Models Using High Frequency Data
Posted: 18 Aug 2006 Last revised: 27 Feb 2013
Date Written: August 1, 2006
This paper 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 based on the observed state variables over extended horizons. With the estimates of the latent variables, we propose a 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, latent state variables, unbiased minimum-variance estimator, generalized method of moments, high frequency data
JEL Classification: C13, C22
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