An integrated model for forecasting system load

Box and Jenkins’ consider the properties of a class of linear stochastic models which are of value in representing stationary and non-stationary time series and show how these models may be used for forecasting. The practical problems of identification, fitting and diagnostic checking are applied to a variety of series. In particular, the methods are used to analyse and forecast seasonal series. In general, a series is said to exhibit periodic behaviour with period s when similarities in the series occur after s basic time intervals. The basic time interval might be one month and the period is s = 12 months or it might be s = 4 for quarterly data. It sometimes happens that there is more than one periodicity. Box and Jenkins provide an exhaustive discussion of the identification, estimation and forecasting of seasonal models. That discussion need not be repeated here. One factor that is characteristic of their analysis is that the estimated autoregressive and moving parameters are constant over the entire period of estimation. For a situation when the series is being estimated over short horizons, say one or two months or a quarter, the values of the parameters will be stable. If the series is being estimated over a longer period encompassing a change in season, then variations in the autoregressive and/or moving average parameters should be taken into account. Accounting for such variations is the objective of this paper. To facilitate the analysis a model similar to that constructed for the airline passenger data of Box and Jenkins will be used. In the present instance, the data consist of monthly peak system loads for an electric utility.