Bringing an elementary agent-based model to the data: Estimation via GMM and an application to forecasting of asset price volatility

We explore the issue of estimating a simple agent-based model of price formation in an asset market using the approach of Alfarano et al. (2008) as an example. Since we are able to derive various moment conditions for this model, we can apply generalized method of moments (GMM) estimation. We find that we can get relatively accurate parameter estimates with an appropriate choice of moment conditions and initialization of the iterative GMM estimates that reduce the biases arising from strong autocorrelations of the estimates of certain parameters. We apply our estimator to a sample of long records of returns of various stock and foreign exchange markets as well the price of gold. Using the estimated parameters to form the best linear forecasts for future volatility we find that the behavioral model generates sensible forecasts that get close to those of a standard GARCH (1,1) model in their overall performance, and often provide useful information on top of the information incorporated in the GARCH forecasts.