Scandinavian Working Papers in Economics
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The Economic Research Institute, Stockholm School of Economics SSE/EFI Working Paper Series in Economics and Finance

No 79:
Parameter Estimation and Reverse Martingales

Tomas Björk () and Bjorn Johansson

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.

Keywords: Parameter estimation; time reversal; martingale theory; (follow links to similar papers)

JEL-Codes: C13; (follow links to similar papers)

33 pages, October 1995

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This paper is published as:
Björk, Tomas and Björn Johansson, (1996), 'Parameter Estimation and Reverse Martingales', Stochastic Processes and their Applications, Vol. 63, pages 235-263

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