A note on minimizing absolute percentage error in combined forecasts

In this note, two new approaches of combined forecasts are proposed. One approach minimizes mean absolute percentage error while the other approach minimizes the maximum absolute percentage error. A goal programming model is used to obtain the weights to combine different forecasts to minimize the mean absolute percentage error. This formulation can be solved readily by any linear programming computer code. The other approach, minimizing the maximum absolute percentage error, can also be formulated as a goal programming model. Scope and purposeMean absolute percentage error has been widely used as a performance measure in forecasting. One of the major reasons for its popularity is that it is easy to interpret and understand and it becomes a good alternative to mean squared error. Our proposed linear programming models can provide solutions of the minimum mean absolute percentage error and the minimum of the maximum absolute percentage error in combined forecasts. The models we proposed could be solved readily by any linear programming computer code.

[1]  Sunil Gupta,et al.  Combination of Forecasts: An Extension , 1987 .

[2]  C. E. Love,et al.  Classifying and controlling errors in forecasting using multiple criteria goal programming , 1994, Comput. Oper. Res..

[3]  GuptaSunil,et al.  Combination of Forecasts , 1987 .

[4]  H. W. Mui,et al.  Forecasting the spot price of gold:combined forecast approaches versus a composite forecast approach , 1993 .

[5]  R. L. Winkler,et al.  Combining Economic Forecasts , 1986 .

[6]  D. W. Bunn,et al.  A Bayesian Approach to the Linear Combination of Forecasts , 1975 .

[7]  Edna M. White,et al.  Subjective versus objective combining of forecasts: An experiment , 1989 .

[8]  Sevket I. Gunter,et al.  N‐step combinations of forecasts , 1989 .

[9]  Gary R. Reeves,et al.  Combining multiple forecasts given multiple objectives , 1982 .

[10]  E. Adam,et al.  An empirical evaluation of alternative forecasting combinations , 1987 .

[11]  Gary R. Reeves,et al.  Combining forecasts given different types of objectives , 1991 .

[12]  K. Wall,et al.  A preference-based method for forecast combination , 1989 .

[13]  Sunil Gupta,et al.  Combination of Economic Forecasts: An Odds-Matrix Approach , 1988 .

[14]  R. L. Winkler,et al.  Averages of Forecasts: Some Empirical Results , 1983 .

[15]  Heejoon Kang.  Unstable Weights in the Combination of Forecasts , 1986 .

[16]  C. Granger,et al.  Experience with Forecasting Univariate Time Series and the Combination of Forecasts , 1974 .

[17]  R. H. Edmundson,et al.  The accuracy of combining judgemental and statistical forecasts , 1986 .