A Novel Approach for Combined Forecasting Model Systems Based on the Correlation Coefficient Ranking of the Individual Forecasting Models


  • Lily Ingsrisawang Department of Statistics, Faculty of Science, Kasetsart University, Bangkok, Thailand
  • Chantha Wongoutong Department of Statistics, Faculty of Science, Kasetsart University, Bangkok, Thailand


Combined forecasting method, correlation coefficient, model weighting, stationary


This study investigates the efficiency of forecasting by two combined forecasting model methods (simple-average and Bates-Granger) comprising up to five individual forecasting models. The novel approach of ranking the correlation coefficients between the predicted values produced by the individual forecasting model and the actual values is used to rank the individual forecasting models used in the combined forecasting model methods. The results of a simulation study and using real datasets with a stationary pattern time series demonstrate that the simple-average and Bates-Granger combined approaches based on the two highest-ranked individual forecasting models improved the forecasting performance better than with five, four, or three individual forecasting models, especially for a short time-series dataset. Hence, the novel approach using two vital individual models in their correlation coefficients for combined forecasting produces fewer errors and improves the forecasting accuracy than 3-5 individual models in the combined forecasting approach.


Ahmed NK, Atiya AF, Gayar NE, El-Shishiny H. An empirical comparison of machine learning models for time series forecasting. Econom Rev. 2010; 29(5-6): 594-621.

Armstrong JS. Principles of forecasting: a handbook for researchers and practitioners. New York: Kluwer Academic Publishers; 2001.

Bates JM, Granger CW. The combination of forecasts. J Oper Res Soc.1969; 20(4): 451-468.

Box GE, Jenkins GM, Reinsel G. Time series analysis: forecasting and control. New Jersey: Prentice-Hall; 1994.

Box GE, Jenkins GM, Reinsel G. Forecasting and control. J Time Ser Anal. 1970; 3(75): 1970.

Box GE, Jenkins GM, Reinsel GC, Ljung GM. Time series analysis: forecasting and control. New York: John Wiley & Sons; 2015.

Brown RG. Exponential smoothing for predicting demand. Cambridge: Arthur D. Little; 1956.

Clements M, Hendry D. Forecasting economic time series. Cambridge University Press; 1998.

Cortez P, Rocha M, Neves J. Evolving time series forecasting ARMA models. J Heuristics. 2004; 10: 415-429.

Cortes C, Vapnik V. Support-vector networks. Mach Learn. 1995; 20: 273-297.

De Menezes LM, Bunn DW, Taylor JW. Review of guidelines for the use of combined forecasts. Eur J Oper Res. 2000; 120(1): 190-204.

Holt CC. Forecasting seasonals and trends by exponentially weighted moving averages. Int J Forecast. 2004; 20(1): 5-10.

Hyndman RJ, Athanasopoulos G. Forecasting: principles and practice. Melbourne: OTexts; 2018.

Jose VR, Winkler RL. Simple robust averages of forecasts: Some empirical results. Int J Forecast. 2008; 24(1): 163-169.

Karatzoglou A, Hornik K, Smola A, Zeileis A. kernlab-an S4 package for kernel methods in R. J Stat Softw. 2004; 11(9): 1-20, https://doi.org/10.18637/jss.v011.i09.

Khandelwal I, Adhikari R, Verma G. Time series forecasting using hybrid ARIMA and ANN models based on DWT decomposition. Procedia Comput Sci. 2015; 48: 173-179.

Kim KJ. Financial time series forecasting using support vector machines. Neurocomputing. 2003; 55(1-2): 307-319.

Lobo GJ. Analysis and comparison of financial analysts', time series, and combined forecasts of annual earnings. J Bus Res. 1992; 24(3): 269-280.

Makridakis S, Winkler RL. Averages of forecasts: Some empirical results. J Manag Sci. 1983; 29(9): 987-996.

Makridakis S, Hibon M. The M3-Competition: results, conclusions and implications. Int J Forecast. 2000; 16(4): 451-476.

Okasha MK. Using support vector machines in financial time series forecasting. Int J Stat Appl. 2014; 4(1): 28-39.

Sanders NR, Ritzman LP. Some empirical findings on short‐term forecasting: technique complexity and combinations. Decis Sci. 1989; 20(3): 635-640.

Shi HY, Hwang SL, Lee KT, Lin CL. In-hospital mortality after traumatic brain injury surgery: a nationwide population-based comparison of mortality predictors used in artificial neural network and logistic regression models. J Neurosurg. 2013; 118(4): 746-752.

Svetunkov I, Petropoulos F. Old dog, new tricks: a modelling view of simple moving averages. Int J Prod Res. 2018; 56(18): 6034-6047.

Taylor JW, Bunn DW. Investigating improvements in the accuracy of prediction intervals for combinations of forecasts: a simulation study. Int J Forecast 1999; 15(3): 325-339.

Thaithanan, J., Wongoutong, C. A combined forecasting model for predicting the number of road traffic accident deaths in Thailand. ADAS. 2020; 64(2): 143-163.

The R Foundation. The R project for statistical computing. 2020 [cited 2022 Feb 14]. Available

from: http://www.r-project.org/

Timmermann A. Forecast combinations. Handb Econ Forecast. 2006; 1: 135-196.

Stock JH, Watson MW. Combination forecasts of output growth in a seven‐country data set. J Forecast. 2004; 23(6): 405-430.

Wongoutong C. The Effect on forecasting accuracy of the holt-winters method when using the incorrect model on a non-stationary time series. Thail Stat. 2021; 19(3): 565-582.

Yang Y. Combining forecasting procedures: some theoretical results. Econ Theory. 2004; 20(1): 176-222.

Yolcu U, Egrioglu E, Aladag CH. A new linear & nonlinear artificial neural network model for time series forecasting. Decis Support Syst. 2013; 54(3): 1340-1347.

Xiao Z, Wu W. The application of combining forecasting based on PSO-PLS to GDP. J Manag Sci. 2008; 21(3): 115-122.

Zhao CY, Zhang HX, Zhang XY, Liu MC, Hu ZD, Fan BT. Application of support vector machine (SVM) for prediction toxic activity of different data sets. J Toxicol. 2006; 217(2-3): 105-119.




How to Cite

Ingsrisawang, L. ., & Wongoutong, C. . (2023). A Novel Approach for Combined Forecasting Model Systems Based on the Correlation Coefficient Ranking of the Individual Forecasting Models. Thailand Statistician, 21(4), 887–909. Retrieved from https://ph02.tci-thaijo.org/index.php/thaistat/article/view/251067