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Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ‐optimality

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  • Martin Jacobsen

Abstract

Ergodic diffusions in several dimensions, depending on an unknown multivariate parameter are considered. For estimation, when the diffusion is observed only at finitely many equidistant time points, unbiased estimating functions leading to consistent and asymptotically Gaussian estimators are used. Different types of estimating functions are discussed and the concept of small Δ‐optimality is introduced to help select good estimating functions. Explicit criteria for small Δ‐optimality are given. Also some exact optimality conditions are presented as well as, for one‐dimensional diffusions, methods for improving estimators using time reversibility.

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  • Martin Jacobsen, 2001. "Discretely Observed Diffusions: Classes of Estimating Functions and Small Δ‐optimality," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 28(1), pages 123-149, March.
    • Handle: RePEc:bla:scjsta:v:28:y:2001:i:1:p:123-149
    DOI: 10.1111/1467-9469.00228
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    Cited by:

    1. Friedrich Hubalek & Petra Posedel, 2008. "Asymptotic analysis for a simple explicit estimator in Barndorff-Nielsen and Shephard stochastic volatility models," Papers 0807.3479, arXiv.org.
    2. Nina Munkholt Jakobsen & Michael Sørensen, 2015. "Efficient Estimation for Diffusions Sampled at High Frequency Over a Fixed Time Interval," CREATES Research Papers 2015-33, Department of Economics and Business Economics, Aarhus University.
    3. Michael Sørensen, 2008. "Efficient estimation for ergodic diffusions sampled at high frequency," CREATES Research Papers 2007-46, Department of Economics and Business Economics, Aarhus University.
    4. Helle Sørensen, 2002. "Parametric Inference for Diffusion Processes Observed at Discrete Points in Time: a Survey," Discussion Papers 02-08, University of Copenhagen. Department of Economics.
    5. Mathieu Kessler & Michael Sørensen, 2005. "On Time-Reversibility and Estimating Functions for Markov Processes," Statistical Inference for Stochastic Processes, Springer, vol. 8(1), pages 95-107, January.
    6. Jakobsen, Nina Munkholt & Sørensen, Michael, 2019. "Estimating functions for jump–diffusions," Stochastic Processes and their Applications, Elsevier, vol. 129(9), pages 3282-3318.
    7. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    8. Per Aslak Mykland & Lan Zhang, 2006. "ANOVA for diffusions and It\^{o} processes," Papers math/0611274, arXiv.org.
    9. Chang, Jinyuan & Chen, Songxi, 2011. "On the Approximate Maximum Likelihood Estimation for Diffusion Processes," MPRA Paper 46279, University Library of Munich, Germany.
    10. Friedrich Hubalek & Petra Posedel, 2011. "Joint analysis and estimation of stock prices and trading volume in Barndorff-Nielsen and Shephard stochastic volatility models," Quantitative Finance, Taylor & Francis Journals, vol. 11(6), pages 917-932.
    11. Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.

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