Métodos estadísticos clásicos y bayesianos para el pronóstico de demanda. Un análisis comparativo
Classical and bayesian statistical methods for demand forecasting. A comparative analysis
DOI:
https://doi.org/10.15446/rev.fac.cienc.v4n1.49775Keywords:
Pronósticos, métodos bayesianos, distribución predictiva (es)Forecast, bayesian methods, predictive distribution (en)
Downloads
La industria usualmente requiere mejores técnicas que permitan elaborar buenos planes de producción. En presencia de pocos datos históricos, pueden presentarse dicultades en el cumplimiento de premisas teóricas. En este artículo se presenta una comparación a partir de un estudio de simulación, diseñado en el programa R con el propósito de realizar la elección del mejor modelo: Regresión lineal bayesiana con distribución a priori normal, modelo lineal dinámico bayesiano, modelo ARIMA y modelo de suavización exponencial, con base en el criterio Mean Absolute Percentage Error (MAPE) de pronóstico y para ello se simulan diferentes esquemas de datos que re ejan comportamientos de demandas con y sin distribución normal. De las simulaciones se encuentran casos en que se prefiere la estimación bayesiana, en lugar de la clásica. Se encuentra que los modelos bayesianos estudiados tienen un alto potencial para realizar predicciones, sobre todo para los datos que no se comportan con una distribución normal, siendo más precisos que los otros modelos clásicos comparados, además son más robustos a premisas teóricas y se pueden utilizar con pocos datos históricos.
Comparisons between forecast models are necessary for decision making in industry, especially for demand prediction. In the presence of few historical data, there could be diffculties in the compliance of theoretical premises. In this paper, a comparison is presented designed in R program, using four types of models: Bayesian linear regression with normal prior distribution, bayesian dynamic linear model, ARIMA and exponential smoothing, based on criteria: Mean Absolute Percentage Error (MAPE) of forecasts, and therefore different data scenarios are simulated, reflecting demand behavior with and without Normal Distribution and with or without dynamic variance. Bayesian models under study were found to have a high potential in predictions, especially for data that does not behave with a normal distribution, being more precise than the other classical models compared, besides, they are more robust to theoretical premises, and they can be used with few historical data.
References
Barrera, C., & Correa, J. (2008). Distribución predictiva bayesiana para modelos de pruebas de vida vía MCMC. Revista Colombiana de Estadística, 31(2), 145–155.
Bermúdez, J. D., Segura, J. V, & Vercher, E. (2009). Bayesian forecasting with the Holt–Winters model. Journal of the Operational Research Society, 61(1), 164–171.
Bijak, J. (2005). Bayesian Methods in International migration forecasting (p.30). Polonia. doi:83-921915-5-2
Bolstad, W. M. (1986). Harrison-Stevens Forecasting and the Multiprocess Dynamic Linear Model. The American Statistician, 40(2), 129-135.
Bowerman, B. L., Bowerman, B. L. K., O'Connell, A. B., & Richard, T. (2007).Forecasting, time series, and regression: an applied approach. Pronósticos, series de tiempo y regresión: un enfoque aplicado/. México, DF:. CENCAGE Learning.
Bowerman, B. L. & Oconnell, R. T. (2007). Pronósticos, series de tiempo y regresión: un enfoque aplicado. (C. L. Editores., Ed.) (p. 693). México.
Caridad & Ocerin, J. M. (1998). Econometria: Modelos Econométricos y series temporales. (R.S.A., Ed.).
Carriero, A., Kapetanios, G., & Marcellino, M. (2009). Forecasting exchange rates with a large Bayesian VAR. International Journal of Forecasting, 25(2), 400-417. doi:10.1016/j.ijforecast.2009.01.007
Choi, T., Li, D., & Yan, H. (2003). Optimal two-stage ordering policy with Bayesian information updating. Journal of the operational research society, 54(8), 846-859. doi:10.1057/palgrave.jors.2601584
Cogley, T.; Morozov, S. & Sargent, T. J. (2003). Bayesian Fan Charts for U . K . Inflation: Forecasting and Sources of Uncertainty in an Evolving Monetary System (pp. 1-40).
Congdon, P. (2002). Bayesian Statistical Modelling. (U. of London, Ed.) (p. 529). London, England: Wiley Series in Probability and Statistics.
Correa, A. & Gómez, R. (2009). Tecnologías de la Información en la Cadena de Suministro. DYNA, 76(157), 37-48.
Diebold, F. (1999). Elementos de pronósticos. México: International Thomson editores.
Duncan, G., Gorr, W., & Szczypula, J. (1993). Bayesian forecasting for seemingly unrelated time series: Application to local government revenue forecasting. Management Science, 39(3), 275-293.
Flora Lu, Q. (2005). Bayesian Forecasting of Stock Prices, Via the Ohlson Model., (May), 80. Retrieved from https://www.wpi.edu/Pubs/ETD/Available/etd-050605-
/unrestricted/Flora Thesis May 2005.pdf
Gelman, A.; Carlin, J. B.; Stern, H. S. & Rubin, D. B. (2004). Bayesian Data Analysis. (C. & Hall, Ed.) (Second Edi., p. 668).
Gill, J. (2007). Bayesian methods: A social and behavioral sciences approach (Second., p. 459). United States of America: CHapman & Hall.
Lee, J.; Boatwright, P. & Kamakura, W. A. (2003). A Bayesian Model for Prelaunch Sales Forecasting of Recorded Music, 49(2), 179-196.
Makridakis, S.; Hibon, M.; Moser, C.; Journal, S.; Statistical, R. & Series, S. (2011). Accuracy of Forecasting?: An Empirical Investigation. Journal of the Royal Statistical Society, 142(2), 97-145.
Meinhold, R. J. & Singpurwalla, N. D. (1983). Understanding the Kalman Filter. The American Statistician, 37(2), 123-127.
Mol, C. De; Giannone, D. & Reichlin, L. (2008). Forecasting using a large number of predictors: Is Bayesian shrinkage a valid alternative to principal components? Journal of Econometrics, 146(2), 318-328.
Neelamegham, R. & Chintagunta, P. (1999). A Bayesian model to forecast new product performance in domestic and international markets. Marketing Science, 18(2), 115-136.
Nenes, G.; Panagiotidou, S. & Tagaras, G. (2010). Inventory management of multiple items with irregular demand: A case study. European Journal of Operational Research, 205(2), 313-324. doi:10.1016/j.ejor.2009.12.022
Qun, H. & Wei, S. (2010). Research on Optimization Algorithm of Data Flow Forecasting Analysis Based on ARIMA Model. 2010 International Conference on Challenges in Environmental Science and Computer Engineering, 463466. doi:10.1109/CESCE.2010.189
R Core Team. (2014). A Language and Environment for Statistical Computing. Vienna, Austria: R Foundation for Statistical Computing. Retrieved from http://www.r-project.org/
Samaratunga, C.; Sethi, S. & Zhou, X. (1997). Computational evaluation of hierarchical production control policies for stochastic manufacturing systems. Operations Research, 45(2), 258274. Retrieved from http://or.journal.informs.org/content/45/2/258.short
Sarimveis, H.; Patrinos, P.; Tarantilis, C. D. & Kiranoudis, C. T. (2008). Dynamic modeling and control of supply chain systems: A review. Computers & Operations Research, 35(11), 3530-3561. doi:10.1016/j.cor.2007.01.017
Sloughter, J. M. L.; Raftery, A. E.; Gneiting, T. & Fraley, C. (2007), Probabilistic quantitative precipitation forecasting using Bayesian model averaging. Monthly Weather Review, 135(9), 3209-3220.
Tabares, J.; Velásquez, C. & Valencia, M. (2014). Comparación de técnicas estadísticas de pronóstico para la demanda de energía eléctrica. Revista de Ingeniería Industrial, 13(1), 1931. doi:07188307
Valencia, M. & Correa, J. (2013). Un modelo dinámico bayesiano para pronóstico de energía diaria. Revista Ingeniería Industrial, 12(2), 7-17.
Valencia, M.; Díaz, F. J. & Correa, J. C. (2015). Planeación de inventarios con demanda dinámica . Una revisión del estado del arte. Revista DYNA, 82(190), 182-191. doi:http://dx.doi.org/10.15446/dyna.v82n190.42828
Valencia, M.; Ramírez, S.; Tabares, J. & Velásquez, C. (2014). Métodos de pronóstico clásicos y bayesianos con aplicaciones (p. 89). Universidad Nacional de Colombia. En: http://www.bdigital.unal.edu.co/.
Ventura, J. A.; Valdebenito, V. A. & Golany, B. (2013). A dynamic inventory model with supplier selection in a serial supply chain structure. European Journal of Operational Research, 230(2), 258-271. doi:10.1016/j.ejor.2013.03.012
Wang, S. (2006). Exponential Smoothing for Forecasting and Bayesian Validation of Computer Models. (Georgia Institute of Technology, Ed.) (p. 233).
Wang, W.; Rivera, D. E. & Kempf, K. G. (2005). A novel model predictive control algorithm for supply chain management in semiconductor manufacturing. Proceedings of the 2005, American Control Conference, 2005., Jun 8-10., 208-213. doi:10.1109/ACC.2005.1469933
Watson, R. (1987). The eects of demand-forecast fluctuations on customer service and inventory cost when demand is lumpy. Journal of the Operational Research Society, 38(1), 75-82.
Weinberg, J.; Brown, L. D. & Stroud, J. R. (2007). Bayesian Forecasting of an Inhomogeneous Poisson Process with Applications to Call Center Data. Journal of the American Statistical Association, 102(480), 1185-1198.
West, M. & Harrison, J. (1997). Bayesian Forecasting and Dynamic Models (Vol 18., p. 704). Springer Series in Statistics.
Wilson, J. H.; Keating, B. & Galt, J. (2007). Pronósticos en los negocios (Fifth Ed., p. 461). McGraw-Hill.
Yelland, P. M. (2010). Bayesian forecasting of parts demand. International Journal of Forecasting, 26(2), 374-396. doi:10.1016/j.ijforecast.2009.11.001
Yelland, P. M. & Lee, E. (2003). Forecasting Product Sales with Dynamic Linear Mixture Models. Sun Microsystems (p. 22).
How to Cite
APA
ACM
ACS
ABNT
Chicago
Harvard
IEEE
MLA
Turabian
Vancouver
Download Citation
CrossRef Cited-by
1. Brenda Díaz-Landa, Rosana Meleán-Romero, William Marín-Rodriguez. (2021). Rendimiento académico de estudiantes en Educación Superior: predicciones de factores influyentes a partir de árboles de decisión. Telos Revista de Estudios Interdisciplinarios en Ciencias Sociales, 23(3), p.616. https://doi.org/10.36390/telos233.08.
2. Johan Sebastian Ibañez Ramírez, Tatiana Echeverri Salazar , Omar Danilo Castrillón Gómez. (2021). Predicción de la calidad de vida universitaria a través de minería de datos . Revista Ingenierías Universidad de Medellín, 21(40), p.1. https://doi.org/10.22395/rium.v21n40a1.
Dimensions
PlumX
Article abstract page views
Downloads
License
The authors or copyright holders of each paper confer to the Journal of the Faculty of Sciences of Universidad Nacional de Colombia a non-exclusive, limited and free authorization on the paper that, once evaluated and approved, is sent for its subsequent publication in accordance with the following characteristics:
- The corrected version is sent according to the suggestions of the evaluators and it is clarified that the paper mentioned is an unpublished document on which the rights are authorized and full responsibility is assumed for the content of the work before both the Journal of the Faculty of Sciences, Universidad Nacional de Colombia and third parties.
- The authorization granted to the Journal will be in force from the date it is included in the respective volume and number of the Journal of the Faculty of Sciences in the Open Journal Systems and on the Journal’s home page (https://revistas.unal.edu.co/index.php/rfc/index), as well as in the different databases and data indexes in which the publication is indexed.
- The authors authorize the Journal of the Faculty of Sciences of Universidad Nacional de Colombia to publish the document in the format in which it is required (printed, digital, electronic or any other known or to be known) and authorize the Journal of the Faculty of Sciences to include the work in the indexes and search engines deemed necessary to promote its diffusion.
- The authors accept that the authorization is given free of charge, and therefore they waive any right to receive any emolument for the publication, distribution, public communication, and any other use made under the terms of this authorization.
- All the contents of the Journal of the Faculty of Sciences are published under the Creative Commons Attribution – Non-commercial – Without Derivative 4.0.License
MODEL LETTER OF PRESENTATION and TRANSFER OF COPYRIGHTS
Personal data processing policy
The names and email addresses entered in this Journal will be used exclusively for the purposes set out in it and will not be provided to third parties or used for other purposes.