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Estimation for diffusion processes from discrete observation

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  • Yoshida, Nakahiro
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    Abstract

    The maximum likelihood estimation of the unknown parameter of a diffusion process based on an approximate likelihood given by the discrete observation is treated when the diffusion coefficients are unknown and the condition for "rapidly increasing experimental design" is broken. The asymptotic normality of the joint distribution of the maximum likelihood estimator of the unknown parameter in the drift term and an estimator of the diffusion coefficient matrix is proved. We prove the weak convergence of the likelihood ratio random field, which serves to show the asymptotic behavior of the likelihood ratio tests with restrictions.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 41 (1992)
    Issue (Month): 2 (May)
    Pages: 220-242

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    Handle: RePEc:eee:jmvana:v:41:y:1992:i:2:p:220-242

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    Related research

    Keywords: diffusion process discrete observation diffusion coefficient likelihood ratio maximum likelihood estimator;

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    Citations

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    Cited by:
    1. Stan Hurn & J.Jeisman & K.A. Lindsay, 2006. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations. Working paper #2," NCER Working Paper Series 2, National Centre for Econometric Research.
    2. Nakahiro Yoshida, 2011. "Polynomial type large deviation inequalities and quasi-likelihood analysis for stochastic differential equations," Annals of the Institute of Statistical Mathematics, Springer, vol. 63(3), pages 431-479, June.
    3. Guy, Romain & Larédo, Catherine & Vergu, Elisabeta, 2014. "Parametric inference for discretely observed multidimensional diffusions with small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 124(1), pages 51-80.
    4. Phillips, Peter C.B. & Yu, Jun, 2009. "A two-stage realized volatility approach to estimation of diffusion processes with discrete data," Journal of Econometrics, Elsevier, vol. 150(2), pages 139-150, June.
    5. A. S. Hurn & J. I. Jeisman & K. A. Lindsay, 0. "Seeing the Wood for the Trees: A Critical Evaluation of Methods to Estimate the Parameters of Stochastic Differential Equations," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 5(3), pages 390-455.
    6. Yoshida, Nakahiro, 2013. "Martingale expansion in mixed normal limit," Stochastic Processes and their Applications, Elsevier, vol. 123(3), pages 887-933.
    7. Sangyeol Lee & Hiroki Masuda, 2010. "Jarque–Bera normality test for the driving Lévy process of a discretely observed univariate SDE," Statistical Inference for Stochastic Processes, Springer, vol. 13(2), pages 147-161, June.
    8. J. Jimenez & R. Biscay & T. Ozaki, 2005. "Inference Methods for Discretely Observed Continuous-Time Stochastic Volatility Models: A Commented Overview," Asia-Pacific Financial Markets, Springer, vol. 12(2), pages 109-141, June.
    9. Masuda, Hiroki, 2013. "Asymptotics for functionals of self-normalized residuals of discretely observed stochastic processes," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2752-2778.
    10. Gloter, Arnaud & Sørensen, Michael, 2009. "Estimation for stochastic differential equations with a small diffusion coefficient," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 679-699, March.
    11. Alessandro DE GREGORIO & Stefano Maria IACUS, 2011. "On a family of test statistics for discretely observed diffusion processes," Departmental Working Papers 2011-37, Department of Economics, Management and Quantitative Methods at Università degli Studi di Milano.
    12. Arnaud Gloter, 2007. "Efficient estimation of drift parameters in stochastic volatility models," Finance and Stochastics, Springer, vol. 11(4), pages 495-519, October.
    13. Masayuki Uchida, 2010. "Contrast-based information criterion for ergodic diffusion processes from discrete observations," Annals of the Institute of Statistical Mathematics, Springer, vol. 62(1), pages 161-187, February.
    14. Samson, Adeline & Thieullen, Michèle, 2012. "A contrast estimator for completely or partially observed hypoelliptic diffusion," Stochastic Processes and their Applications, Elsevier, vol. 122(7), pages 2521-2552.
    15. Michael Sørensen, 2008. "Efficient estimation for ergodic diffusions sampled at high frequency," CREATES Research Papers 2007-46, School of Economics and Management, University of Aarhus.
    16. Shoji, Isao, 1997. "A note on asymptotic properties of the estimator derived from the Euler method for diffusion processes at discrete times," Statistics & Probability Letters, Elsevier, vol. 36(2), pages 153-159, December.
    17. Uchida, Masayuki & Yoshida, Nakahiro, 2013. "Quasi likelihood analysis of volatility and nondegeneracy of statistical random field," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2851-2876.
    18. Uchida, Masayuki, 2008. "Approximate martingale estimating functions for stochastic differential equations with small noises," Stochastic Processes and their Applications, Elsevier, vol. 118(9), pages 1706-1721, September.
    19. Comte, F. & Genon-Catalot, V. & Rozenholc, Y., 2009. "Nonparametric adaptive estimation for integrated diffusions," Stochastic Processes and their Applications, Elsevier, vol. 119(3), pages 811-834, March.

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