Fig. 1. The structure of an NXCS expert, which embeds a genetic guard and a neural predictor.

Fig. 2. A feedforward ANN for stock market forecasting, with 10 numerical inputs and 3 outputs.

Fig. 3. Overall system architecture.

Fig. 4. Economic results on the COMIT stock market index (For color see online version).

Fig. 5. Economic results on the S&P500 stock market index (For color see online version).

Fig. 6. The basic scheme of an XCS system.

Table 1. Definitions of technical-analysis indicators

Table 2. Binary inputs, to be matched by the guard of an NXCS expert

Table 3. Inputs to the ANN

Table 4. Major parameters' values used for the NXCS subsystem

Table 5. Comparing economic results for the COMIT and S&P500 stock market indexes

TS = trading strategy, CV = cumulative value (in euro), AR% = percent of annualized returns, CP = commission paid (in euro), IC = interest collected (in euro), σ = standard deviation, S = sharpe ratio, and ω = merit factor.

Table 6. Comparing predictive capabilities of LRANNs- and NXCSs-based systems

PT = prediction technique, CC = percent of correct classifications, ip% = ideal profit, L/S = long vs. short signal statistics).

Table 7. Gain and loss statistics, evaluated on a mobile window of 30 trading days

TS = trading strategy, AR% = percent of annualized returns, σ = standard deviation.

Table 8. Gain and loss statistics, evaluated on a mobile window of 100 trading days

TS = trading strategy, AR% = percent of annualized returns, σ = standard deviation.

Table 9. Widrow–Hoff rules used for updating the most important parameters of an XCS classifier (the parameter β controls the “inertial” behavior of the update)