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Computers & Operations Research 28 (2001) 1141}1147

Note

A note on minimizing absolute percentage error in combined forecasts

K.F. Lam*, H.W. Mui, H.K. Yuen

Department of Management Sciences, City University of Hong Kong, 83 Tat Chee Avenue, Kowloon, Hong Kong Received 1 March 1998; received in revised form 1 June 1999

Abstract 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 di!erent 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 purpose Mean 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. 2001 Elsevier Science Ltd. All rights reserved.

Keywords: Goal programming; Combined forecasts

1. Introduction Many authors suggest that combined forecasts will outperform a single forecast approach (see, for example, Makridakis and Winkler [1], Lawrence et al. [2] and Russel and Adam [3]). They

* Corresponding author. Fax: #852-2788-8560. E-mail address: msblam@cityu.edu.hk (K.F. Lam). 0305-0548/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 3 0 5 - 0 5 4 8 ( 0 0 ) 0 0 0 2 6 - 5

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