Comparação de previsões individuais e suas combinações: um estudo com séries industriais
Comparison of individual forecasts and their combinations: a study with industrial series
Martins, Vera Lucia M.; Werner, Liane
http://dx.doi.org/10.1590/S0103-65132013005000066
Production, vol.24, n3, p.618-627, 2014
Resumo
A necessidade de realizar previsões acuradas, oriunda do crescente aprimoramento tecnológico, tem estimulado a aplicação e comparação de diferentes técnicas de modelagem, assim como de métodos de combinação. Historicamente, pesquisadores consideram que combinar previsões originadas de diferentes técnicas melhora a sua acurácia, embora alguns estudos questionem se essa é realmente a melhor opção. Este trabalho procura verificar, para previsões industriais, se há diferença entre a acurácia das previsões individuais e a de suas combinações, por meio da modelagem de séries reais. Como técnicas de previsão individual, utilizam-se a metodologia Box-Jenkins e a modelagem RNA; para a combinação das previsões, utilizam-se os métodos da média aritmética e da variância mínima simplificado. A avaliação de desempenho das previsões é obtida por meio das medidas de acurácia MAPE, MSE e MAE. Como principal resultado, destaca-se a frequência predominante em que previsões obtidas pelo método da variância mínima apresentaram desempenho superior em relação às demais previsões.
Palavras-chave
Previsão. Acurácia. Combinação
Abstract
Technological development has increased the necessity for more accurate predictions that stimulate the application and comparison of modeling techniques and methods of combination. Historically, researchers have believed that combining forecasts from different techniques improves the forecasts, but some studies question whether combining is really the best option. This paper aims to verify whether there is a difference between the accuracy of individual forecasts and that of their combinations by modeling real industrial prediction series. The Box-Jenkins methodology and ANN modeling were used for individual forecasting, whereas the simplified minimum variance and mean arithmetic methods were used for forecast combinations. The performance of the predictions was evaluated by MAPE (Mean Absolute Percentual Error), MSE (Mean Square Error) and MAE (Mean Absolute Error). As the main result, we highlight the predominant frequency at which the predictions obtained by the minimum variance method show superior performance compared to other forecasts.
Keywords
Forecasting. Accuracy. Combining
References
ABRAHAM, B.; LEDOLTER, J. Statistical Methods for Forecasting. New York: John Wiley & Sons, 2005.
ANDERSON-CONNELL, L. J.; ULRICH, P. V.; BRANNON, E. L. A consumer-driven model for mass customization in apparel market. Journal of Fashion Marketing and Management, v. 6, n. 3, p. 240-258, 2002. http://dx.doi.org/10.1108/13612020210441346
ANDRAWIS, R. R.; ATIYA, A. F.; EL-SHISHINY, H. Combination of long term and short term forecasts, with application to tourism demand forecasting. International Journal of Forecasting, v. 27, n. 3, p. 870-886, 2011. http://dx.doi.org/10.1016/j.ijforecast.2010.05.019
ARMSTRONG, J. S. Principles of forecasting: A handbook for researchers and practitioners. Kluwer Academic Publishers. 2001. http://dx.doi.org/10.1007/978-0-306-47630-3
ARMSTRONG, J. S.; COLLOPY, F. Integration of Statistical Methods and Judgments of Time Series Forecasting: Principles for Empirical Research. In: WRIGHT, G.; GOODWIN, P. Forecasting with Judgment. Wiley & Sons, 1998.
AUER, P.; BURGSTEINER, H.; MAASS, W. A learning rule for very simple universal approximators consisting of a single layer of perceptrons. Neural Networks, v. 21, p. 786-795, 2008. PMid:18249524. http://dx.doi.org/10.1016/j.neunet.2007.12.036
BATES, J. M.; GRANGER, C. W. J. The combination of forecasts. Operational Research Quarterly, v. 20, n. 4, p. 451-468, 1969. http://dx.doi.org/10.1057/jors.1969.103
BOX, G. E. P.; JENKINS, G. M. Time series analysis. San Francisco: Holden-Day, 1976.
BOX, G. E. P.; JENKINS, G. M.; REINSEL, G. C. Time Series Analysis, Forecasting and Control. 3rd ed. Englewood Clifs: Prentice Hall, 1994. 598 p.
CHEN, K. Y.; WANG, C. H. A hybrid SARIMA and support vector machines in forecasting the production values of the machinery industry in Taiwan. Expert Systems with Applications, v. 32, n. 1, p. 254-264, 2007. http://dx.doi.org/10.1016/j.eswa.2005.11.027
CLARK, K. B.; FUJIMOTO, T. Product development performance: strategy, organization and management in the world auto industry. Boston: Harvard Business School Press, 1991.
CLARK, K. B.; WHEELWRIGTH, S. C. Managing New Product and Process Development: text and cases. New York: The Free Press, 1993. 896 p.
CLEMEN, R. T. Combining forecasts: A review and annotated bibliography. International journal of forecasting, v. 5, p. 559-583, 1989. http://dx.doi.org/10.1016/0169-2070(89)90012-5
CLEMEN, R. T.; WINKLER, R. L. Combining economic forecasts. Journal of Business and Economic Estatistics, v. 4, p. 39-46, 1986.
COSTANTINE, C.; PAPPALARDO, C. A hierarchical procedure for combination of forecasts. International journal of forecasting, v. 26, p. 725-743, 2010. http://dx.doi.org/10.1016/j.ijforecast.2009.09.006
DE WILDE, P. Neural networks models: theory and projects. 2. ed. New York: Springer-Verlag, 1997. 174 p.
FLORES, B. E.; WHITE, E. M. Combining forecasts: why, when and how. Journal of Business Forecasting Methods & Systems, v. 8, n. 3, p. 2-5, 1989.
FLORES, J. H. F. Comparação de modelos MLP/RNA e modelos Box-Jenkins em séries temporais não lineares. 2009. Dissertação (Mestrado em Engenharia de Produção)-Universidade Federal do Rio Grande do Sul, Porto Alegre, 2009.
GARCIA, E. et al. Gestão de Estoques: Otimizando a logística e a cadeia de suprimentos. Rio de Janeiro: E-Papers Serviços Editoriais, 2006. 144 p.
GILMORE, J. H.; PINE II, J. B. Markets of one: creating customer-unique value through mass customization. Boston: Harvard Business School Press, 2000.
GOODWIN, P.; LAWTON, R. On the asymmetry of the symmetric MAPE. International journal of forecasting, v. 15, p. 405-408, 1999. http://dx.doi.org/10.1016/S0169-2070(99)00007-2
HAIR JUNIOR, J. F. et al. Análise multivariada de dados. 5. ed. Porto Alegre: Bookman, 2005. 593 p.
HAYKIN, S. Redes neurais: princípios e prática. 2. ed. Porto Alegre: Bookman, 2001. 900 p.
HIBON, M.; EVGENIOU, T. To combine or not to combine: selecting among forecasts and their combinations. International Journal of Forecasting, v. 21, p. 15-24, 2005. http://dx.doi.org/10.1016/j.ijforecast.2004.05.002
HOLLAUER, G.; ISSLER, J. V.; NOTINI, H. H. Prevendo o crescimento da produção industrial usando um número limitado de combinações de previsões. Economia Aplicada, v. 12, n. 2, p. 177-198, 2008. http://dx.doi.org/10.1590/S1413-80502008000200001
KHASHEI, M.; BIJARI, M. An artificial neural network (p, d, q) model for timeseries forecasting. Expert Systems with Applications, v. 37, p. 479-489, 2010. http://dx.doi.org/10.1016/j.eswa.2009.05.044
KONIG, A. J. et al. The M3-Competition: Statistical tests of the results. International Journal of Forecasting, v. 21, p. 397-409, 2005. http://dx.doi.org/10.1016/j.ijforecast.2004.10.003
MAKRIDAKIS, S. G.; HIBON, M. The M3-Competition: results, conclusions and implications. International Journal of Forecasting, v. 16, p. 451-476, 2000. http://dx.doi.org/10.1016/S0169-2070(00)00057-1
MAKRIDAKIS, S. G.; WHEELWRIGHT, S. C.; HYNDMAN, R. J. Forecasting: methods and applications. 3. ed. Wiley, 1998. 642 p.
MAKRIDAKIS, S. G.; WINKLER, R. L. Averages of Forecasts: Some empirical results. Menagement Science, v. 29, p. 987-996, 1983. http://dx.doi.org/10.1287/mnsc.29.9.987
MENEZES, L. M.; BUNN, D. W.; TAYLOR, J. W. Review of guidelines for the use combined forecast. European Journal of Operational Research, v. 120, p. 190-204, 2000. http://dx.doi.org/10.1016/S0377-2217(98)00380-4
MORETTIN, P. A.; TOLOI, C. M. C. Análise de séries temporais. 2 ed. rev. ampl. São Pulo: Edgard Blücher, 2006. 538 p.
MÜLLER, B.; REINHARDT, J.; STRICKLAND, M. T. Neural networks: an introduction. 2. ed. New York: Springer-Verlag, 1995. 330 p.
NEWBOLD, P.; GRANGER, C. W. J. Experience with forecasting univariate time series and the combination of forecasts. Journal of the Royal Statistical Society. Series A (General), v. 137, n. 2, p. 131-165, 1974. http://dx.doi.org/10.2307/2344546
PATTON, A. J.; SHEPPARD, K. Optimal combinations of realised volatility estimators. International Journal of Forecasting, v. 25, 2009, p. 218-238. http://dx.doi.org/10.1016/j.ijforecast.2009.01.011
QI, M.; ZHANG, G. P. An investigation of model section criteria for neural network time series forecasting. European Journal of Operational Research, v. 132, p. 666-680, 2001. http://dx.doi.org/10.1016/S0377-2217(00)00171-5
RIPLEY, B. D. Pattern recognition and neural networks. Cambridge: Cambridge University Press, 1996. 415 p.
PALIWAL, M.; KUMAR, U. A. Neural networks and statistical techniques: A review of applications. Expert Systems with Applications, v. 36, p. 2-17, 2009. http://dx.doi.org/10.1016/j.eswa.2007.10.005
SLACK, N. et al. Administração da Produção. 2. ed. São Paulo: Atlas, 2007.
STOCK, J. H.; WATSON, M. W. Combination forecasts of output growth in a seven-country data set. Journal of Forecasting, v. 23, p. 405-430, 2004. http://dx.doi.org/10.1002/for.928
TIMMERMANN, A. Forecast Combinations. In: ELLIOTT, G.; GRANGER, C. W. J.; TIMMERMANN, A. Handbook of Economic Forecasting. San Diego: North-Holland, 2006. v. 1.
WEBBY, R.; O'CONNOR, M. Judgemental and statistical time series forecasting: a review of the literature. International Journal of Forecast, v. 12, p. 91-118, 1996. http://dx.doi.org/10.1016/0169-2070(95)00644-3
WERNER, L. Um modelo composto para realizar previsão de demanda através da integração da combinação e de previsões e ajuste baseado na opinião. 2005. Tese (Doutorado)-Universidade Federal do Rio Grande do Sul, Porto Alegre, 2005.
WERNER, L.; RIBEIRO, J. L. D. Previsão de demanda: uma aplicação dos modelos Box-Jenkins na área de assistência técnica de computadores pessoais. Gestão e Produção, v. 10, n. 1, p. 47-67, 2003. http://dx.doi.org/10.1590/S0104-530X2003000100005
WONG, K. K. F. et al. Tourism forecasting: To combine or not to combine?. Tourism management, v. 28, p. 1068-1078, 2007. http://dx.doi.org/10.1016/j.tourman.2006.08.003
YANG, Y. Combining forecasts procedures: Some theoretical results. Econometric Theory, v. 20, p. 176-190, 2004. http://dx.doi.org/10.1017/S0266466604201086
ZHANG, G. P.; BERARDI, V. L. Time series forecasting with neural network ensembles: an application for exchange rate prediction. Journal of Operational Research Society, v. 52, p. 652-664, 2001. http://dx.doi.org/10.1057/palgrave.jors.2601133