Artículos regulares

 

Modelos de regresión para el pronóstico de series temporales con estacionalidad creciente

 

Regression Models for Time Series with Increasing Seasonality

 

Sergio David Madrigal Espinoza

 

División de Estudios de Posgrado, FIME, UANL, San Nicolás de los Garza, NL, México. sergio.madrigales@uanl.edu.mx

 

Article received on 16/09/2013.
Accepted on 01/09/2014.

 

Resumen

Se compara el desempeño de tres modelos de regresión, en términos de su efectividad predictiva, para el caso de series temporales con estacionalidad creciente. Se emplearon 617 series en el cotejo así como tres modelos de los cuales, uno es propuesta original de este trabajo. Adicionalmente, se compararon estos modelos contra uno de raíces unitarias, típicamente empleado para el pronóstico de las series de interés. Entre los resultados más importantes, se muestra que la efectividad de los modelos de regresión dependerá del horizonte de pronóstico así como del grado de su curvatura. A menor curvatura y mayor horizonte, mejor será su desempeño. Se mostrarán las condiciones bajo las cuales, los modelos de regresión pueden pronosticar tan bien o incluso mejor que la alternativa típica. Por último, se realiza un análisis de los intervalos de predicción y sobre cómo mejorar su efectividad.

Palabras clave: Modelos de regresión, series temporales, estacionalidad, econometría.

 

Abstract

In this paper, three regression models are compared according to their performance in terms of forecast accuracy, for the case of time series with increasing seasonality. 617 series are used in the comparison as well as three models, being one of them an original contribution of this work. In addition, the regression models are compared with the autoregressive approach, commonly used in the forecast of these series. The results indicate that the performance of the regression models depends on the forecast horizon and on the degree of curvature of the series. At fewer curvature and longer forecast horizon, its performance is better. The conditions under which the regression models outperform the autoregressive approach are discussed. Also, the performance of the prediction intervals in order to improve its effectiveness is analyzed.

Keywords: Regression models, time series, seasonality, econometrics.

 

DESCARGAR ARTÍCULO EN FORMATO PDF

 

Referencias

1. Akram, M., Hyndman, R. J., & Ord, J. K. (2009). Exponential smoothing and non-negative data. Australian and New Zealand Journal of Statistics, Vol. 51, No. 4, pp. 415-432.         [ Links ]

2. Bowerman, B. L., Koehler, A. B., & Pack, D. J. (1990). Forecasting time series with increasing seasonal time variation. Journal of Forecasting, Vol. 9, pp. 419-436.         [ Links ]

3. Box, G. E. P., Jenkins, G. M., & Reinsell, G. C. (2008). Time series analysis: Forecasting and Control. WILEY, 4 edition.         [ Links ]

4. Chatfield, C. & Prothero, D. L. (1973). Box jenkins seasonal forecasting: Problems in a case study (with discussion). Journal of The Royal Statistical Socity A, Vol. 136, pp. 295-336.         [ Links ]

5. Cleveland, W. S. (1983). Seasonal and calendar adjustment. In Handbook of Statistics, volume 3. Elsevier Science Publishers B.V., 39-72.         [ Links ]

6. Dagum, E. B. (1982). Revisions of time varying seasonal filters. Journal of Forecasting, Vol. 1, pp. 20-28.         [ Links ]

7. Franses, P. H. (1996). Recent advances in modeling seasonality. Journal of Economic Surveys, Vol. 10, pp. 299-345.         [ Links ]

8. Franses, P. H. & Koehler, A. B. (1998). A model selection strategy for time series with increasing seasonal variation. International Journal of Forecasting, Vol. 14, No. 3, pp. 405-414.         [ Links ]

9. Ghysels, E. (1991). Are business cycle turning points uniformly distributed throughout the year? Cahiers de recherche 9135, Universite de Montreal, Departement de sciences economiques.         [ Links ]

10. Ghysels, E. (1994). On the periodic structure of the business cycle. Journal of Business and Economic Statistics, Vol. 12, pp. 289-293.         [ Links ]

11. Hylleberg, S., Engle, R. F., Granger, C. W. J., & Yoo, B. S. (1990). Seasonal integration and cointegration. Journal of Econometrics, Vol. 44, No. 1-2, pp. 215-238.         [ Links ]

12. Hyndman, R. J. (2012). Mcomp: Data from the M-competitions. R package version 2.04.         [ Links ]

13. Hyndman, R. J., Koehler, A. B., Ord, J. K., & Snyder, R. D. (2005). Prediction intervals for exponential smoothing state space models. International Journal of Forecasting, Vol. 24, pp. 17-37.         [ Links ]

14. Hyndman, R. J., Koehler, A. B., Ord, J. K., & Snyder, R. D. (2008). Forecasting with Exponential Smoothing: The State Space Approach. Springer, 1 edition.         [ Links ]

15. Ihaka, R. & Gentleman, R. (1996). R: A language for data analysis and graphics. Journal of Computational and Graphical Statistics, Vol. 5, No. 3, pp. 299-314.         [ Links ]

16. Koehler, A. B., Snyder, R. D., & Ord, J. K. (2001). Forecasting models and prediction intervals for the multiplicative holt-winters method. International Journal of Forecasting, Vol. 17, pp. 269-286.         [ Links ]

17. Madrigal Espinoza, S. D. (2011). Pronóstico de series temporales con estacionalidad. Tesis Doctoral, Universidad Autónoma de Nuevo León.         [ Links ]

18. Makridakis, S., Andersen, A., Carbone, R., Fildes, R., Hibon, M., Lewandowski, R., Newton, J., Parzen, E., & Winkler, R. (1982). The accuracy of extrapolation (time series) methods: Results of a forecasting competition. Journal of Forecasting, Vol. 1, No. 2, pp. 111-153.         [ Links ]

19. Makridakis, S., Wheelwright, S. C., & Hyndman, R. J. (1998). Forecasting Methods and Applications. John Wiley, 3 edition.         [ Links ]

20. Novales, A. & de Fruto, R. D. (1997). Forecasting with periodic models: A comparison with the time invariant coefficient models. International Journal of Forecasting, Vol. 13, pp. 393-405.         [ Links ]

21. Ord, J. K., Koehler, A. B., & Snyder, R. D. (1997). Estimation and prediction for a class of dynamic nonlinear statistical models. Journal of American Statistical Association, Vol. 92, pp. 1621-1629.         [ Links ]

22. Team, R. C. (2012). R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria.         [ Links ]

23. Wells, J. M. (1997). Modelling seasonal patterns and long-run trends in U.S. time series. International Journal of Forecasting, Vol. 13, pp. 407-420.         [ Links ]

24. Wooldridge, J. M. (2001). Introducción a la Econometría. Thomson Learning.         [ Links ]