Testing of a market fraction model and power-law behaviour in the DAX 30

•We test a simple market fraction asset pricing model with heterogeneous agents.•We select structural parameters of the model through a systematic procedure.•The volatility of the model shares the same decay patterns with the DAX 30.•The (FI)GARCH parameters and the tail index of the model match those of the DAX 30.•The results strongly support the explanatory power of the HAMs.

This paper tests a simple market fraction asset pricing model with heterogeneous agents. By selecting a set of structural parameters of the model through a systematic procedure, we show that the autocorrelations (of returns, absolute returns and squared returns) of the market fraction model share the same pattern as those of the DAX 30. By conducting econometric analysis via Monte Carlo simulations, we characterize these power-law behaviours and find that estimates of the power-law decay indices, the (FI)GARCH parameters, and the tail index of the selected market fraction model closely match those of the DAX 30. The results strongly support the explanatory power of the heterogeneous agent models.