Step-by-step Combining of Individual Forecasts Based on the Granger-Ramanathan Method

Abstract

The article is devoted to the problem of increasing the accuracy of forecasting by combining individual forecasts. It presents a modification of one of the most popular forecast combination methods proposed by Granger and Ramanathan, which is based on minimizing the prediction error. These methods are often used in practical calculations. However, they can give negative coefficients and, thus, some weights may exceed one. The paper considers a modification of the methodology based on the use of an iterative procedure in order to exclude the negative weights from combining the forecasts. The authors carried out comparative analysis of both the proposed method and the traditional Granger-Ramanathan combination with restrictions on weights summing to one, and individual forecasts on the basis of which the combining is performed. The comparison was made on the basis of time series on the production of a number of types of products in physical terms.  The results of the study made it possible to conclude that the proposed modification of the Granger-Ramanathan method using sequential prediction does slightly reduce its accuracy, but it saves the approach in question from negative weighting coefficients. As a result it broadens the applicability of the real practice-oriented forecasting.