Specification of a forecasting system

Abstract

This thesis incorporates the compilation and derivation of the theory required for an interactive forecasting system. The techniques employed are those of statistical time series analysis. It is shown that the generating function approach given by Whittle (1963) for the prediction of stationary processes, can also be applied to non-stationary autoregressive integrated moving-average (ARIMA) models. Using this approach an alternative representation is given for the forecast function of an integrated moving average process which is simpler than the direct basic form of Godolphin (1975). These models have polynomial-projecting predictors, with or without a forward-shifted forecast function. The derivation is also extended to include an autoregressive parameter of order one to give a forecast function which also contains an asymptotic component. The inclusion of a non-zero mean for the ARIMA process gives a modified form for the forecast function. The result suggests a technique which is applicable to intervention problems. It allows the user, who could be a non-specialist or specialist practitioner, to interact with the modelling process at any time stage to take account of available prior knowledge. This procedure is analogous with the Bayesian Forecasting intervention techniques, associated with Harrison and Stevens (1976), but it simplifies the mathematical complications without reducing its applicability. The final part of the study incorporates classical inference techniques for analysing the data series with these forecasting procedures. An interactive forecasting system for three non-seasonal univariate models is considered with the emphasis falling on simplicity of manipulation.