Scandinavian Working Papers in Economics

SSE/EFI Working Paper Series in Economics and Finance,
Stockholm School of Economics

No 79: Parameter Estimation and Reverse Martingales

Tomas Björk () and Bjorn Johansson
Additional contact information
Tomas Björk: Department of Finance, Postal: Stockholm School of Economics, Box 6501, 113 83 Stockholm, Sweden.

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

JEL-codes: C13

33 pages, October 1995

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