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An Approximate Innovation Method For The Estimation Of Diffusion Processes From Discrete Data

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  • J. C. Jimenez
  • T. Ozaki

Abstract

. In this paper, an approximate innovation method is introduced for the estimation of diffusion processes, given a set of discrete and noisy observations of some of their components. The method is based on a recent extension of local linearization filters to the general case of continuous–discrete state–space models with multiplicative noise. This filtering method provides adequate approximations for the prediction and filter estimates that are required by the innovation method in the estimation of the unknown parameters and the unobserved component of the diffusion process. The performance of approximate innovation estimators is illustrated by means of numerical simulations.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:1:p:77-97
    DOI: 10.1111/j.1467-9892.2005.00454.x
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Brigo, Damiano & Hanzon, Bernard, 1998. "On some filtering problems arising in mathematical finance," Insurance: Mathematics and Economics, Elsevier, vol. 22(1), pages 53-64, May.
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    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. Quentin J M Huys & Liam Paninski, 2009. "Smoothing of, and Parameter Estimation from, Noisy Biophysical Recordings," PLOS Computational Biology, Public Library of Science, vol. 5(5), pages 1-16, May.

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