Maximum likelihood estimation for integrated diffusion processes
AbstractWe 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.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-33.
Date of creation: 05 Aug 2010
Date of revision:
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Web page: http://www.econ.au.dk/afn/
Diffusion bridge; discretely sampled diffusions; EM-algorithm; likelihood inference; measurement error; stochastic differential equation; stochastic volatility.;
Find related papers by JEL classification:
- C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models &bull Diffusion Processes
- C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
This paper has been announced in the following NEP Reports:
- NEP-ALL-2010-09-03 (All new papers)
- NEP-ECM-2010-09-03 (Econometrics)
- NEP-ETS-2010-09-03 (Econometric Time Series)
- NEP-ORE-2010-09-03 (Operations Research)
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