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Comparative study of estimation methods for continuous time stochastic processes

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  • Isao Shoji
  • Tohru Ozaki

Abstract

In this paper we investigate the finite sample performances of five estimation methods for a continuous‐time stochastic process from discrete observations. Applying these methods to two examples of stochastic differential equations, one with linear drift and state‐dependent diffusion coefficients and the other with nonlinear drift and constant diffusion coefficients, Monte Carlo experiments are carried out to evaluate the finite sample performance of each method. The Monte Carlo results indicate that the differences between the methods are large when the discrete‐ time interval is large. In addition, these differences are noticeable in estimations of the diffusion coefficients.

Suggested Citation

  • Isao Shoji & Tohru Ozaki, 1997. "Comparative study of estimation methods for continuous time stochastic processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 18(5), pages 485-506, September.
    • Handle: RePEc:bla:jtsera:v:18:y:1997:i:5:p:485-506
    DOI: 10.1111/1467-9892.00064
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    Cited by:

    1. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    2. A. S. Hurn & K. A. Lindsay & A. J. McClelland, 2015. "Estimating the Parameters of Stochastic Volatility Models Using Option Price Data," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 33(4), pages 579-594, October.
    3. 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;Japanese Association of Financial Economics and Engineering, vol. 12(2), pages 109-141, June.
    4. Yvo Pokern & Andrew M. Stuart & Petter Wiberg, 2009. "Parameter estimation for partially observed hypoelliptic diffusions," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 71(1), pages 49-73, January.
    5. Eva María Ramos-Ábalos & Ramón Gutiérrez-Sánchez & Ahmed Nafidi, 2020. "Powers of the Stochastic Gompertz and Lognormal Diffusion Processes, Statistical Inference and Simulation," Mathematics, MDPI, vol. 8(4), pages 1-13, April.
    6. Peter C.B.Phillips & Jun Yu, "undated". "Maximum Likelihood and Gaussian Estimation of Continuous Time Models in Finance," Working Papers CoFie-08-2009, Singapore Management University, Sim Kee Boon Institute for Financial Economics.
    7. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.
    8. Otunuga Olusegun M. & Ladde Gangaram S. & Ladde Nathan G., 2019. "Local Lagged Adapted Generalized Method of Moments: An Innovative Estimation and Forecasting Approach and its Applications," Journal of Time Series Econometrics, De Gruyter, vol. 11(1), pages 1-72, January.
    9. Stramer, O., 1999. "The local linearization scheme for nonlinear diffusion models with discontinuous coefficients," Statistics & Probability Letters, Elsevier, vol. 42(3), pages 249-256, April.
    10. Hermann Singer, 2003. "Simulated Maximum Likelihood in Nonlinear Continuous-Discrete State Space Models: Importance Sampling by Approximate Smoothing," Computational Statistics, Springer, vol. 18(1), pages 79-106, March.
    11. Cysne, Rubens Penha, 2004. "On the Statistical Estimation of Diffusion Processes: A Partial Survey," Brazilian Review of Econometrics, Sociedade Brasileira de Econometria - SBE, vol. 24(2), November.
    12. Qinwen Zhu & Hui Liu & Chengfeng Sun, 2019. "Edgeworth Expansion For The Distribution Of The Maximum Likelihood Estimate In The Vasicek Model," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 14(01), pages 1-26, March.
    13. Alejandra López-Pérez & Manuel Febrero-Bande & Wencesalo González-Manteiga, 2021. "Parametric Estimation of Diffusion Processes: A Review and Comparative Study," Mathematics, MDPI, vol. 9(8), pages 1-27, April.
    14. 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, Oxford University Press, vol. 5(3), pages 390-455.
    15. 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.
    16. Hermann Singer, 2011. "Continuous-discrete state-space modeling of panel data with nonlinear filter algorithms," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 95(4), pages 375-413, December.
    17. Hermann Singer, 2006. "Moment equations and Hermite expansion for nonlinear stochastic differential equations with application to stock price models," Computational Statistics, Springer, vol. 21(3), pages 385-397, December.

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