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Efficient Computation of the Quasi Likelihood function for Discretely Observed Diffusion Processes

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  • Lars Josef Hook
  • Erik Lindstrom

Abstract

We introduce a simple method for nearly simultaneous computation of all moments needed for quasi maximum likelihood estimation of parameters in discretely observed stochastic differential equations commonly seen in finance. The method proposed in this papers is not restricted to any particular dynamics of the differential equation and is virtually insensitive to the sampling interval. The key contribution of the paper is that computational complexity is sublinear in the number of observations as we compute all moments through a single operation. Furthermore, that operation can be done offline. The simulations show that the method is unbiased for all practical purposes for any sampling design, including random sampling, and that the computational cost is comparable (actually faster for moderate and large data sets) to the simple, often severely biased, Euler-Maruyama approximation.

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  • Lars Josef Hook & Erik Lindstrom, 2015. "Efficient Computation of the Quasi Likelihood function for Discretely Observed Diffusion Processes," Papers 1509.07751, arXiv.org.
    • Handle: RePEc:arx:papers:1509.07751
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    References listed on IDEAS

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    1. 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.
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    4. 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.
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    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. 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.
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