Distribution forecasting of nonlinear time series with associative memories

The forecasting of financial variables is a problem which has been investigated ever since economies began to develop. Modern day information technology now provides at the fingertips of forecasters an enormous range of historical data, automated forecasts and news stories. In addition to assisting with traditional financial forecasting problems this has allowed financial time series to be investigated at a much higher frequency. The sampling of financial time series at intra-day frequency introduces further complications to forecasting than traditional problems. However, it makes available much larger sets of historical data. This thesis examines the utility of existing forecasting methodology for high frequency forecasting. It then tries to understand what information is provided by past high frequency data and how data intensive algorithms could use it. This thesis also investigates the area of distribution forecasting where the aim is to produce a full probability density forecast rather than a single value. This is a recent addition to the financial forecasting world, encouraged by modern computing power and the large volumes of historical data now available. High frequency data sets have made possible new approaches to distribution forecasting and it is natural to bring the two together. During this work a new approach to the problem is constructed. An algorithm requiring fast k-NN type search is implemented using AURA, a binary neural network based upon Correlation Matrix Memories. This novel architecture also constructs probability distribution forecasts, the volume of data allowing this to be done in a nonparametric manner. Financial forecasting is part of the larger problem of nonlinear forecasting and the new algorithm is therefore tested not only on financial data but other standard forecasting data sets. In addition to standard statistical error measures the implementation of simulations allows actual measures of profit to be calculated. The creation of distribution forecasts introduces difficulties in forecast evaluation and results are reported from a separate evaluation of distribution accuracy.