Fig. 1. Training. The CMM is updated to learn the relationship between the input and the features (clusters). The frequency store holds a historical simulation for each cluster.

Fig. 2. Forecasting. A recall on the CMM produces the nearest neighbours from which the forecast is constructed. Each neighbour has its own distribution in the frequency store.

Fig. 3. The effect of the window size and number of bins on the ADA error measure. The x and y axes show the parameter values and the z axis shows the error value.

Fig. 4. The effect of the window size and number of bins on the Theil's U statistic error measure. The x and y axes show the parameter values and the z axis shows the error value.

Fig. 5. The effect of the window size and number of bins on the simulation return. The x and y axes show the parameter values and the z axis shows the return.

Fig. 6. The effect of lowering the recall threshold on forecast accuracy and the number of features used. The average given is the mean number of features used per forecasts over the whole test set.

Fig. 7. Iterative extension using the distribution forecast. All possible values given by the previous forecast are treated as observations to make a possible forecast for one further step ahead. An average of all possible forecasts combines them to a single forecast. The weighted average is calculated by the probability given by the distributions of the series following that path.

Fig. 8. The effect of extending k on forecast accuracy.

Table 1. The effect of lowering the recall threshold on forecast accuracy for a range of parameter sets

Table 2. A comparison of different techniques for forecast extension

Table 3. Results of check that the training distributions and test distributions are samples of the same distribution

The Mann–Whitney and Smirnov tests have been carried out for each feature.