  We replicate the contested calibration of the Farmer and Joshi agent based
model of financial markets using a genetic algorithm and a Nelder-Mead with
threshold accepting algorithm following Fabretti. The novelty of the
Farmer-Joshi model is that the dynamics are driven by trade entry and exit
thresholds alone. We recover the known claim that some important stylized facts
observed in financial markets cannot be easily found under calibration -- in
particular those relating to the auto-correlations in the absolute values of
the price fluctuations, and sufficient kurtosis. However, rather than concerns
relating to the calibration method, what is novel here is that we extended the
Farmer-Joshi model to include agent adaptation using an Brock and Hommes
approach to strategy fitness based on trading strategy profitability. We call
this an adaptive Farmer-Joshi model: the model allows trading agents to switch
between strategies by favouring strategies that have been more profitable over
some period of time determined by a free-parameter fixing the profit monitoring
time-horizon. In the adaptive model we are able to calibrate and recover
additional stylized facts, despite apparent degeneracy's. This is achieved by
combining the interactions of trade entry levels with trade strategy switching.
We use this to argue that for low-frequency trading across days, as calibrated
to daily sampled data, feed-backs can be accounted for by strategy die-out
based on intermediate term profitability; we find that the average trade
monitoring horizon is approximately two to three months (or 40 to 60 days) of
trading.
