On the use of backward difference formulae to improve the prediction of direction in market related data

The use of a BDF method as a tool to correct the direction of predictions made using curve fitting techniques is investigated. Random data is generated in such a fashion that it has the same properties as the data we are modelling. The data is assumed to have "memory" such that certain information imbedded in the data will remain within a certain range of points. Data within this period where "memory" exists - say at time steps t1,t2,.,tn - is curve-fitted to produce a prediction at the next discrete time step, tn+1. In this manner a vector of predictions is generated and converted into a discrete ordinary differential representing the gradient of the data. The BDF method implemented with this lower order approximation is used as a means of improving upon the direction of the generated predictions. The use of the BDF method in this manner improves the prediction of the direction of the time series by approximately 30%.