The forecasting procedure recently developed by Professors Box and Jenkins, and described in Box and Jenkins (1970), is based on a class of models (A.R.I.M.A. models) capable of representing a wide range of time series. In this thesis we examine some of the practical problems involved in applying the Box-Jenkins procedure to seasonal time series. A Box-Jenkins analysis of a series of sales figures is described in detail and some of the problems encountered during this analysis are dealt with at length. The topics examined include the application of non-linear transformations in time series analyses and the employment of differencing operators as a means of producing a stationary process. The computation of the unconditional sum of squares when estimating the parameters in an A.R.I.M.A. model and the performance of the Box-Jenkins procedure when applied to series which include deterministic components are also investigated. The A.R.I.M.A, model arising when a time series is considered to be generated by stochastic trend, seasonal and extraneous error components is developed while the interpretation of A.R.I.M.A. models, and their generated forecasts, in terms of the more familiar concepts of trend and seasonality, is explored. A summary of 4 further Box-Jenkins analyses is given, special reference being made to the topics mentioned above. The performance of the Box-Jenkins procedure is compared with that of the method proposed by Winters (1960), on the 5 series included in this thesis.
|Date of Award||1975|