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Parametric inference for discretely sampled stochastic differential equations

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  • Michael Sørensen

    (School of Economics and Management, University of Aarhus, Denmark and CREATES)

Abstract

A review is given of parametric estimation methods for discretely sampled multivariate diffusion processes. The main focus is on estimating functions and asymptotic results. Maximum likelihood estimation is briefly considered, but the emphasis is on computationally less demanding martingale estimating functions. Particular attention is given to explicit estimating functions. Results on both fixed frequency and high frequency asymptotics are given. When choosing among the many estimators available, guidance is provided by simple criteria for high frequency efficiency and rate optimality that are presented in the framework of approximate martingale estimating functions.

Suggested Citation

  • Michael Sørensen, 2008. "Parametric inference for discretely sampled stochastic differential equations," CREATES Research Papers 2008-18, Department of Economics and Business Economics, Aarhus University.
    • Handle: RePEc:aah:create:2008-18
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    File URL: https://repec.econ.au.dk/repec/creates/rp/08/rp08_18.pdf
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    References listed on IDEAS

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    Cited by:

    1. Yuichi Nagahara, 2008. "A Method of Calculating the Downside Risk by Multivariate Nonnormal Distributions," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 15(3), pages 175-184, December.

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    More about this item

    Keywords

    Asymptotic results; discrete time observation of a diffusion; efficiency; eigenfunctions; explicit inference; generalized method of moments; likelihood infer- ence; martingale estimating functions; high frequency asymptotics; Pearson diffu- sions.;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C32 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes; State Space Models

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