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Handbook of Financial Time Series pp 531–553Cite as

Parametric Inference for Discretely Sampled Stochastic Differential Equations

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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.

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  1. Department of Mathematical Sciences, University of Copenhagen, Universitetsparken, 5, DK-2100, Copenhagen Ø, Denmark

    Michael Sørensen

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    Sørensen, M. (2009). Parametric Inference for Discretely Sampled Stochastic Differential Equations. In: Mikosch, T., Kreiß, JP., Davis, R., Andersen, T. (eds) Handbook of Financial Time Series. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-71297-8_23

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