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Parametric inference for discretely sampled stochastic differential equations

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Author Info

  • 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 mul- tivariate diffusion processes. The main focus is on estimating functions and asymp- totic 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 estima- tors 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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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2008-18.

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Length: 22
Date of creation: 04 Apr 2008
Date of revision:
Handle: RePEc:aah:create:2008-18

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Web page: http://www.econ.au.dk/afn/

Related research

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.;

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References

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  1. Yacine Ait-Sahalia, 2002. "Closed-Form Likelihood Expansions for Multivariate Diffusions," NBER Working Papers 8956, National Bureau of Economic Research, Inc.
  2. Chan, K C, et al, 1992. " An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, American Finance Association, vol. 47(3), pages 1209-27, July.
  3. Yacine Ait-Sahalia, 2002. "Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-form Approximation Approach," Econometrica, Econometric Society, Econometric Society, vol. 70(1), pages 223-262, January.
  4. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, Econometric Society, vol. 71(2), pages 483-549, March.
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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, Springer, vol. 15(3), pages 175-184, December.

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