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Efficient computation of the quasi likelihood function for discretely observed diffusion processes

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  • Höök, Lars Josef
  • Lindström, Erik

Abstract

An efficient numerical method for nearly simultaneous computation of all conditional moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations is presented. The method is not restricted to any particular dynamics of the stochastic differential equation and is virtually insensitive to the sampling interval. The key contribution is that computational complexity is sublinear in terms of expensive operations in the number of observations as all moments can be computed offline in a single operation. Simulations show that the bias of the method is small compared to the random error in the estimates, and to the bias of comparable methods. Furthermore the computational cost is comparable (actually faster for moderate and large data sets) to the simple, but in some applications badly biased, the Euler–Maruyama approximation.

Suggested Citation

  • Höök, Lars Josef & Lindström, Erik, 2016. "Efficient computation of the quasi likelihood function for discretely observed diffusion processes," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 426-437.
    • Handle: RePEc:eee:csdana:v:103:y:2016:i:c:p:426-437
    DOI: 10.1016/j.csda.2016.05.014
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    References listed on IDEAS

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    1. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    2. Erik Ekstrom & Per Lotstedt & Johan Tysk, 2009. "Boundary Values and Finite Difference Methods for the Single Factor Term Structure Equation," Applied Mathematical Finance, Taylor & Francis Journals, vol. 16(3), pages 253-259.
    3. Pastorello, S. & Rossi, E., 2010. "Efficient importance sampling maximum likelihood estimation of stochastic differential equations," Computational Statistics & Data Analysis, Elsevier, vol. 54(11), pages 2753-2762, November.
    4. Overbeck, Ludger & Rydén, Tobias, 1997. "Estimation in the Cox-Ingersoll-Ross Model," Econometric Theory, Cambridge University Press, vol. 13(3), pages 430-461, June.
    5. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    6. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    7. Yacine Ait--Sahalia & Per A. Mykland, 2003. "The Effects of Random and Discrete Sampling when Estimating Continuous--Time Diffusions," Econometrica, Econometric Society, vol. 71(2), pages 483-549, March.
    8. Varughese, Melvin M., 2013. "Parameter estimation for multivariate diffusion systems," Computational Statistics & Data Analysis, Elsevier, vol. 57(1), pages 417-428.
    9. Ai[dieresis]t-Sahalia, Yacine & Yu, Jialin, 2006. "Saddlepoint approximations for continuous-time Markov processes," Journal of Econometrics, Elsevier, vol. 134(2), pages 507-551, October.
    10. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-762.
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