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The Role of the Likelihood Function in the Estimation of Chaos Models

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  • T. Ozaki
  • J. C. Jimenez
  • V. Haggan‐Ozaki

Abstract

The estimation problem for chaos models defined by deterministic differential equations is discussed, and the important role of the maximum likelihood method in the inferential study of chaos models is highlighted. The usefulness of the likelihood function in the inferential study of chaos is confirmed with numerical examples from the Lorenz chaos model and the Rikitake two disk dynamo chaos model.

Suggested Citation

  • T. Ozaki & J. C. Jimenez & V. Haggan‐Ozaki, 2000. "The Role of the Likelihood Function in the Estimation of Chaos Models," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 363-387, July.
    • Handle: RePEc:bla:jtsera:v:21:y:2000:i:4:p:363-387
    DOI: 10.1111/1467-9892.00189
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    Cited by:

    1. 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.
    2. Arenas, Zochil González & Jimenez, Juan Carlos & Lozada-Chang, Li-Vang & Santana, Roberto, 2021. "Estimation of distribution algorithms for the computation of innovation estimators of diffusion processes," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 187(C), pages 449-467.
    3. J. C. Jimenez & T. Ozaki, 2006. "An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(1), pages 77-97, January.
    4. 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.

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