A method of prediction for non-stationary processes and its application to the problem of load estimation

Abstract

A method of predicting a non-stationary process is described. It is shown that, if the sample functions of the process are expanded in terms of the eigenfunctions of the Loeve and Karhunen integral equation, |the integrated mean square error is a minimum with respect to variations in the eigenfunctions. Furthermore, this minimum error is equal to the sum of the omitted eigenvalues. By means of this expansion, the prediction problem is reduced to that of determining a finite number of coefficients which constitute a set of independent random variables. These coefficients are specified by applying a minimum mean square criterion to a suitable non-linear or linear function of the known parts of the sample function to be extrapolated. The method is also described in terms of discrete or sampled processes and is found to depend on an interesting theorem in matrix algebra. Finally, the method is applied to the problem of estimating the electricity demand in a large area several hours in advance and some results are given.