Maximum likelihood estimation for integrated diffusion processes

Fernando Baltazar-Larios () and Michael Sørensen ()
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Fernando Baltazar-Larios: Universidad Nacional Autónoma de México, Postal: IIMAS, A.P. 20-726, 01000 Mexico, D.F., Mexico
Michael Sørensen: University of Copenhagen and CREATES, Postal: Dept. of Mathematical Sciences, Universitetsparken 5, DK-2100 Copenhagen Ø, Denmark

CREATES Research Papers from Department of Economics and Business Economics, Aarhus University

Abstract: We propose a method for obtaining maximum likelihood estimates of parameters in diffusion models when the data is a discrete time sample of the integral of the process, while no direct observations of the process itself are available. The data are, moreover, assumed to be contaminated by measurement errors. Integrated volatility is an example of this type of observations. Another example is ice-core data on oxygen isotopes used to investigate paleo-temperatures. The data can be viewed as incomplete observations of a model with a tractable likelihood function. Therefore we propose a simulated EM-algorithm to obtain maximum likelihood estimates of the parameters in the diffusion model. As part of the algorithm, we use a recent simple method for approximate simulation of diffusion bridges. In simulation studies for the Ornstein-Uhlenbeck process and the CIR process the proposed method works well.

Keywords: Diffusion bridge; discretely sampled diffusions; EM-algorithm; likelihood inference; measurement error; stochastic differential equation; stochastic volatility. (search for similar items in EconPapers)
JEL-codes: C22 C51 (search for similar items in EconPapers)
Pages: 16
Date: 2010-08-05
New Economics Papers: this item is included in nep-ecm, nep-ets and nep-ore
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Citations: View citations in EconPapers (1)

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