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Estimation for discretely observed diffusions using transform functions

Part of: Inference from stochastic processes Stochastic processes Parametric inference

Published online by Cambridge University Press:  14 July 2016

Leah Kelly ,
Eckhard Platen  and
Michael Sørensen
Leah Kelly
Affiliation:
University of Technology Sydney, School of Finance and Economics and School of Mathematical Sciences, PO Box 123, Broadway, NSW 2007, Australia. Email address: leah.kelly@uts.edu.au
Eckhard Platen
Affiliation:
University of Technology Sydney, School of Finance and Economics and School of Mathematical Sciences, PO Box 123, Broadway, NSW 2007, Australia. Email address: eckhard.platen@uts.edu.au
Michael Sørensen
Affiliation:
University of Copenhagen, Department of Applied Mathematics and Statistics, Universitetspraken 5, DK-2100 Copenhagen Ø, Denmark. Email address: michael@math.ku.dk
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Abstract

This paper introduces a new estimation technique for discretely observed diffusion processes. Transform functions are applied to transform the data to obtain good and easily calculated estimators of both the drift and diffusion coefficients. Consistency and asymptotic normality of the resulting estimators is investigated. Power transforms are used to estimate the parameters of affine diffusions, for which explicit estimators are obtained.

Keywords

Discretely observed diffusiontransformation functionaffine diffusion processestimation

MSC classification

Primary: 62M05: Markov processes 62F12: Asymptotic properties of estimators
Secondary: 60G35: Signal detection and filtering 60G10: Stationary processes
Type
Part 2. Estimation methods
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 99 - 118
Copyright
Copyright © Applied Probability Trust 2004 

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