An objective function for simulation based inference on exchange rate data |
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Authors: | Peter Winker Manfred Gilli Vahidin Jeleskovic |
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Institution: | (1) Department of Economics, University of Giessen, Licher Strasse 64, 35394 Giessen, Germany;(2) Department of Econometrics, University of Geneva, and Swiss Finance Institute, 40 Boulevard du Pont-d’Arve, Geneva 4, 1211, Switzerland |
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Abstract: | The assessment of models of financial market behaviour requires evaluation tools. When complexity hinders a direct estimation
approach, e.g., for agent based microsimulation models, simulation based estimators might provide an alternative. In order
to apply such techniques, an objective function is required, which should be based on robust statistics of the time series
under consideration. Based on the identification of robust statistics of foreign exchange rate time series in previous research,
an objective function is derived. This function takes into account stylized facts about the unconditional distribution of
exchange rate returns and properties of the conditional distribution, in particular, autoregressive conditional heteroscedasticity
and long memory. A bootstrap procedure is used to obtain an estimate of the variance-covariance matrix of the different moments
included in the objective function, which is used as a base for the weighting matrix. Finally, the properties of the objective
function are analyzed for two different agent based models of the foreign exchange market, a simple GARCH-model and a stochastic
volatility model using the DM/US-$ exchange rate as a benchmark. It is also discussed how the results might be used for inference
purposes.
Research has been supported by the DFG grant WI 20024/2-1/2. We are indebted to two anonymous referees of this journal, Leigh
Tesfatsion, Patrick Burns and other participants of the CEF’06 conference in Limassol for helpful comments on preliminary
versions of this paper. |
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Keywords: | Indirect estimation Simulation based estimation Exchange rate returns |
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