MODELS FOR PREDICTION AND CONTROL CHAPTER VII. FORECASTING.
Abstract
The article discusses the problem of forecasting using a linear stochastic model appropriate to represent a given time series. The development uses non-seasonal time series for illustration. The articles proceed on the basis that the model is known exactly. In practice the coefficients actually being used will contain errors of estimation. Estimation errors can be ignored since they will not seriously effect the forecasts unless the number of data points, on which the fit is originally based, is small. The minimum mean square error forecasts may be generated very easily from the difference equation which defines the model. A further recursive calculation yields the probability limits for the forecasts. From the point of view of practical computation of the forecasts, the methods based on the difference equation are much easier than other methods. However, to provide insight into the nature of the forecasts generated by the difference equation, two further methods of generating the forecasts are discussed. These are (a) The integrated form where the difference equation is solved explicitly in terms of mathematical function such as polynomials whose coefficients can then be updated as each new observation comes to hand. (b) A form where the forecasts are expressed as a weighted average of past values of the series. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1967
- Accession Number
- AD0650276
Entities
People
- G. M. Jenkins
- George E. P. Box
Organizations
- University of Wisconsin–Madison