An Objective Function for Simulation Based Inference on Exchange Rate Data

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 or complex multifractal 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 GARCHmodel 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 Leigh Tesfatsion, Patrick Bruns and other participants of the CEF’06 conference in Limassol for helpful comments on a preliminary version of this paper. †Department of Economics, University of Giessen. ‡University of Geneva and Swiss Banking Institute.