Recently, there are a number of studies evaluating the performance of the N-type design when applied to fit the real financial data. In a sense, this series of efforts is equivalent to the inquiry into the empirical relevance of heterogeneous agents. In other words, can the heterogeneous-agent models enhance our capability to explain or forecast the real financial dynamics?
In this paper, we give an intensive exploration of the 2-type and 3-type designs. Both the 2-type and 3-type designs have been applied to different financial time series, including the stock index S&P 500 from Jan. 2005 to Jan. 2007, and the foreign exchange rates EUR/US, JPY/US, and NTD/US from Jan. 2006 to Jan. 2008. We first estimate the 2-type models using the real data, and then examine the goodness of fit, R², from the estimated models. Since the model involves quite a few parameters, 12 for the 2-type models and 15 for the 3-type models, and some parameters are not even continuous, it makes the direct econometric estimation, such as least squares, become infeasible. Therefore, the models have to be estimated using numerical optimization algorithm, such as genetic algorithms.

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