Estimates by bootstrap interval for time series forecasts obtained by theta model

Main Article Content

Daniel Steffen
Anselmo Chaves Neto


In this work, are developed an experimental computer program in Matlab language version 7.1 from the univariate method for time series forecasting called Theta, and implementation of resampling technique known as computer intensive "bootstrap" to estimate the prediction for the point forecast obtained by this method by confidence interval. To solve this problem built up an algorithm that uses Monte Carlo simulation to obtain the interval estimation for forecasts. The Theta model presented in this work was very efficient in M3 Makridakis competition, where tested 3003 series. It is based on the concept of modifying the local curvature of the time series obtained by a coefficient theta (Θ). In it's simplest approach the time series is decomposed into two lines theta representing terms of long term and short term. The prediction is made by combining the forecast obtained by fitting lines obtained with the theta decomposition. The results of Mape's error obtained for the estimates confirm the favorable results to the method of M3 competition being a good alternative for time series forecast.

Article Details



ASSIMAKOPOULOS, V.; NIKOLOPOULOS, K. (2000) The theta model: a decomposition approach to forecasting. International Journal of Forecasting v. 16, p. 521–530.

ASSIMAKOPOULOS, V.; NIKOLOPOULOS, K. (2008) Advances in the theta model. University of Peloponnese, Department of Economics.

BOUCHER, T. O.; ELSAYED, E. A. (1994) Analysis and control of production systems., 2.nd ed., Prentice Hall, New Jersey.

CHAVES NETO, A. (1991) Bootstrap” em Séries Temporais. Thesi (PhD in Eletric Engineering) – Pontifícia Universidade Catolica do Rio de Janeiro. PUC-RJ.

DAVISON, A. C.; HINKLEY, D. V. (1997) Bootstrap Methods and their Application. Cambridge University Press.

EFRON, B. (1979) Bootstrap methods: another look at jakknife. Annals of Statisticis, v. 7, n. 1, p. 1-26.

EFRON, B.; TIBSHIRANI, R. J. (1993) An introduction to the “bootstrap”. Chapman and Hall, New York.

GUTIÉRRES, J. L. C. (2003) Monitoramento da Instrumentação da Barragem de Corumba-I por Redes Neurais e Modelos de Box e Jenkins. Dissertation (Master in Civil Engineering), PUC-RIO.

HESTERBERG, T.; MOORE, D. S.; MONAGHAN, S.; CLIPSON, A.; EPSTEIN, R. (2003) "Bootstrap” methods and permutation tests, In: The practice of business statistics. New York: W. H. Freeman.

HYNDMAN, R. J.; BILLAH, B. (2003) Unmasking the Theta method. International Journal of Forecasting, v. 19, n. 2, p. 287-290.

LIEBEL, M. J. (2004) Previsão de Receitas Tributárias – O caso do ICMS no Estado do Paraná. Dissertation (Professional Master’s degree in Engineering) – Universidade Federal do Rio Grande do Sul – RS.

MAKRIDAKIS, S.; HIBON, M. (2000) The M3-Competition: results, conclusions and implications. International Journal of Forecasting, v. 16, p. 451–476.

NIKOLOPOULOS, K.; ASSIMAKOPOULOS, V. (2005) Fathoming the Theta model. In: 25th International Symposium on Forecasting, ISF, San Antonio, Texas, USA.

NIKOLOPOULOS, K.; ASSIMAKOPOULOS, V.; BOUGIOUKOS, N.; LITSA, A.; PETROPOULOS, F. (2011) The Theta model: An essential Forecasting Tool for Supply Chain Planning. Advances in Automation and Robotics, Lecture Notes in Electrical Engineering, n. 123, p. 431-437.

PETROPOULOS, F.; NIKOLOPOULOS, K. (2013) Optimizing Theta model for monthly data. In: Proceedings of the 5th International Conference on Agents and Artificial Intelligence.