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Parameter Estimation and Reverse Martingales

Author

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  • Björk, Tomas

    (Department of Finance)

  • Johansson, Bjorn

Abstract

Within the framework of transitive sufficient processes we investigate identifiability properties of unknown parameters. In particular we consider unbiased parameter estimators, which are shown to be closely connected to time reversal and to reverse martingales. One of the main results is that, within our framework, every unbiased estimator process is a reverse martingale, thus automatically giving us strong consistency results. We also study structural properties of unbiased estimators, and it is shown that the existence of an unbiased parameter estimator is equivalent to the existence of a solution to an inverse boundary value problem. We give explicit representation formulas for the estimators in terms of Feynman-Kac type representations using complex valued diffusions, and we also give Cramér-Rao bounds for the estimation error.

Suggested Citation

  • Björk, Tomas & Johansson, Bjorn, 1995. "Parameter Estimation and Reverse Martingales," SSE/EFI Working Paper Series in Economics and Finance 79, Stockholm School of Economics.
    • Handle: RePEc:hhs:hastef:0079
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    References listed on IDEAS

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    1. Björk, Tomas & Johansson, Björn, 1992. "Adaptive prediction and reverse martingales," Stochastic Processes and their Applications, Elsevier, vol. 43(2), pages 191-222, December.
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    Cited by:

    1. Raquel M. Gaspar & Mariana Khapko, 2023. "In memoriam: Tomas Björk (1947–2021)," Finance and Stochastics, Springer, vol. 27(4), pages 867-885, October.

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    1. Raquel M. Gaspar & Mariana Khapko, 2023. "In memoriam: Tomas Björk (1947–2021)," Finance and Stochastics, Springer, vol. 27(4), pages 867-885, October.

    More about this item

    Keywords

    Parameter estimation; time reversal; martingale theory;
    All these keywords.

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

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