A new consensus between the mean and median combination methods to improve forecasting accuracy
Sažetak
To improve the forecasting accuracies, researchers have long been using various combination techniques. In particular, the use of dissimilar methods for forecasting time series data is expected to provide superior results. Although numerous combination techniques have been proposed until date, the simple combination techniques —such as mean and median —maintain their strength, popularity, and utility. This paper proposes a new combination method based on the mean and median combination methods so as to combine the advantages of both these methods. The proposed combination technique attempts to utilize the strong aspects of each method and minimize the risk that arises from the selection of the combination method with poor performance. In order to depict the potential power of the proposed combining method, well-known six real-world time series data were used. Our results indicate that the proposed method presents with promising performances. In addition, a nonparametric statistical test was exploited to reveal the superiority of the proposed method over the single methods and other forecast combination methods from all of the investigated data sets.
Reference
Adhikari, R., & Agrawal, R.K. (2013). A linear hybrid methodology for improving accuracy of time series forecasting. Neural Computing and Applications, 25, 269-281.
Agnew, C. (1985). Bayesian consensus forecasts of macroeconomic variables. Journal of Forecasting, 4, 363-376.
Armstrong, J.S. (2001). Combining forecasts. In: J.S. Armstrong (Eds.). Chapter 13 in Principles of forecasting: a handbook for researchers and practitioners. Kluwer Academic Publishers: Norwell, MA.
Armstrong, S. (1989). Combining forecasts: The end of the beginning or the beginning of the end? International Journal of Forecasting, 5, 585-588.
Bacon, D.W., & Watts, D.G. (1971). Estimating the transition between two intersecting straight lines. Biometrika, 58, 525-534.
Bates, J.M., & Granger, C.W. (1969). The combination of forecasts. Operation Research, 20, 451-468.
Box, G.E.P., & Jenkins, G.M. (1970). Time Series Analysis: Forecasting and Control, San Francisco, Holden Day.
Box, G.E.P., & Jenkins, G.M. (1976). Time Series Analysis, Forecasting and Control. San Francisco: Holden-Day.
Bunn, D.W. (1975). A Bayesian approach to the linear combination of forecasts. Operational Research Quarterly, 26, 325-329.
Cancelo, J.R., & Mourelle, E. (2005). Modeling cyclical asymmetries in GDP: international evidence. Atlantic Economic Journal, 33, 297-309.
Chan, Y.L., Stock, J.H., & Watson, M.W. (1999). A dynamic factor model framework for forecast combination. Spanish Economic Review, 1, 91-121.
Chan, W., Wong, A.C.S., & Tong, H. (2004). Some Nonlinear Threshold Autoregressive Time Series Models for Actuarial Use. North American Actuarial Journal, 8, 37-61.
Clemen, R.T. (1989). Combining forecasts: A review and annotated bibliography. International Journal of Forecasting, 5, 559-583.
De Gooijer, J.G., & Hyndman, R.J. (2006). 25 years of time series forecasting. International Journal of Forecasting, 22, 443-473.
De Groot, C., & Wurtz, D. (1991). Analysis of Univariate Time Series with Connectionist Nets: A Case Study Of Two Classical Examples. Neurocomputing, 3, 177-192.
De Menezes, L.M., Bunn, D.W., & Taylor, J.W. (2000). Review of Guidelines for the Use of Combined Forecasts. European Journal of Operational Research, 120, 190-204.
Deutsch, M., Granger, C.W.J., & Terasvirta, T. (1994). The combination of forecasts using changing weights. International Journal of Forecasting, 10, 47- 57.
Diebold, F.X., & Pauly, P. (1990). The use of prior information in forecast combination. International Journal of Forecasting, 6, 503-508.
Dijk, D.V., Terasvirta, T., & Franses, P.H. (2002). Smooth Transition Autoregressive Models-A Survey of Recent Developments. Econometric Reviews, 21 (1), 1-47.
Faraway, J., & Chatfield, C. (1998). Time Series Forecasting with Neural Networks: A Comparative Study Using the Airline Data. Applied Statistics. 47, 231-250.
Feng, H., & Liu, J. (2003). A SETAR Model for Canadian GDP: Non-linearities and Forecast Comparisons. Applied Economics, 35 (18), 1957-1964.
Fiordaliso, A. (1998). A nonlinear forecast combination method based on Takagi-Sugeno fuzzy systems. International Journal of Forecasting, 14 (3), 367-379.
Franses, P.H., Dijk, D.V., & Opschoor, A. (2014). Time Series Models For Business and Economic Forecasting. New York, NY, USA: Cambridge University Press.
Genre, V., Kenny, G., Meyler, A., & Timmermann, A. (2013). Combining expert forecasts: Can anything beat the simple average? International Journal of Forecasting, 29 (1), 108-121.
Graefe, A., Armstrong, J.S., Jones Jr., R.J., & Cuzán, A.G. (2014). Combining forecasts: An application to elections. International Journal of Forecasting, 30 (1), 43–54.
Hagan, M.T., Demuth, H.B., & Beale, M. (1996). Neural Network Design. Boston: PWS.
Hansen, J.V., McDonald, J.B., & Nelson, R.D. (1999). Time Series Prediction with Genetic-Algorithm Designed Neural Networks: An Empirical Comparison with Modern Statistical Models. Computational Intelligence, 15 (3), 171-184.
Hassan, S., Khosravi, A., Jaafar, J., & Belhaouari, S. (2012). Load forecasting accuracy through combination of trimmed forecasts, in Neural Information Processing, (pp. 152-159). Springer Berlin/ Heidelberg.
Hibon, M., & Evgeniou, T. (2005). To combine or not to combine: Selecting among forecasts and their combinations. International Journal of Forecasting, 21 (1), 15-24.
Hipel, K.W., & McLeod, A.I. (1994). Time Series Modelling of Water Resources and Environmental Systems (Vol. 45). Elsevier.
Hochberg, Y., & Tamhane, A.C. (1987). Multiple Comparison Procedures. Hoboken, NJ: John Wiley & Sons.
Hsu, C.W., & Lin, C.J. (2002). A Comparison of Methods for Multiclass Support Vector Machines. IEEE Transactions on Neural Networks, 13 (2), 415-425.
Hyndman, R.J. (2012). Time Series Data Library. www.robjhyndman.com/TSDL/. (12/06/2012).
Jose, V.R.R., & Winkler, R.L. (2008). Simple robust averages of forecasts: some empirical results.
International Journal of Forecasting, 24 (1), 163-169.
Larreche, J.C., & Moinpour, R. (1983). Managerial judgment in marketing: the concept of expertise. Journal of Marketing Research, 20, 110-121.
Larrick, R., & Soll, J. (2003). Intuitions about combining opinions: Misappreciation of the averaging principle. Working paper INSEAD, 2003/09/TM.
Lemke, C., & Gabrys, B. (2010). Meta-learning for time series forecasting and forecast combination. Neurocomputing, 73 (10), 2006-2016.
Makridakis, S., Wheelwright, S.C., & Hyndman, R.J. (1998). Forecasting Methods and Applications. New York: John Wiley and Sons Ltd.
Makridakis, S., & Winkler, R. (1983). Averages of forecasts: Some empirical results. Management Science, 29 (9), 987-996.
Makridakis, S., Anderson, A., Carbone, R., Fildes, R., Hibdon, 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, 1 (2), 111-153.
Marcellino, M. (2004). Forecast Pooling for Short Time Series of Macroeconomic Variables. Oxford Bulletin of Economic and Statistics, 66 (1), 91-112.
McNees, S.K. (1992). The uses and abuses of ‘consensus’ forecasts. Journal of Forecasting, 11 (8), 703-710.
Miller, C.M., Clemen, R.T., & Winkler, R.L. (1992). The effect of nonstationarity on combined forecasts. International Journal of Forecasting, 7 (4), 515-529.
Newbold, P., & Granger, C.W. (1974). Experience with forecasting univariate time series and the combination of forecasts. Journal of the Royal Statistical Society, 137, 131-165.
Newbold, P., & Harvey, D.I. (2002). Forecast combination and encompassing”. Pp. 268-283 in M.P. Clements & D.F. Hendry (Eds.), A Companion to Economic Forecasting, Oxford: Blackwell Press.
Priestley, M.B. (1988). Non-linear and Non-Stationary Time Series Analysis. San Diego, CA: Academic Press.
Rapach, D.E., Strauss, J.K., & Zhou, G. (2010). Out-of-Sample Equity Premium Prediction: Combination Forecasts and Links to the Real Economy. Review of Financial Studies, 23 (2), 821-862.
Reid, D.J. (1968). Combining three estimates of gross domestic product. Economica, 35 (140), 431-444.
Schauberger, G., & Tutz, G. (2014). Regularization Methods in Economic Forecasting, Advanced Studies in Theoretical and Applied Econometrics. Empirical Economic and Financial Research: Theory, Methods and Practice (pp. 61-80). Switzerland: Springer International Publishing.
Smith, J., & Wallis, K.F. (2009). A Simple Explanation of the Forecast Combination Puzzle. Oxford Bulletin of Economics and Statistics, 71 (3), 331-355.
Stock, J.H., & Watson, M. (1999). A Comparison of Linear and Nonlinear Uni-variate Models for Forecasting Macroeconomic Time Series. Pp. 1-44 in R.F. Engle & H. White (Eds.). Cointegration, Causality, and Forecasting: A Festschrift in Honor of Clive W. J. Granger, Oxford, U.K: Oxford University Press.
Stock, J.H., & Watson, M.W. (1999). Forecasting inflation. Journal of Monetary Economics, 44 (2), 293-375.
Stock, J.H., & Watson, M.W. (2004). Combination forecasts of output growth in a seven-country data set. Journal of Forecasting, 23 (6), 405-430.
Subba Rao, T., & Sabr, M.M. (1984). An Introduction to Bispectral Analysis and Bilinear Time Series Models. New York: Springer-Verlag.
Suykens, J.A., De Brabanter, J., Lukas, L., & Vandewalle, J. (2002). Weighted least squares support vector machines: Robustness and sparse approximation. Neurocomputing, 48 (1), 85-105.
Terasvirta, T., & Anderson, H.M. (1992). Characterizing nonlinearities in business cycles using smooth transition autoregressive models. Journal of Applied Econometrics, 7, 119-136.
Terui, N., & Van Dijk, H.K. (2002). Combined forecasts from linear and nonlinear time series models. International Journal of Forecasting, 18 (3), 421-438.
Timmermann, A. (2006). Forecast combinations. Pp. 135-196 in G. Elliott, C. Granger & A. Timmermann (Eds.), Handbook of Economic Forecasting. Elsevier.
Tong, H. (1978). On a threshold model. Pp. 575-586 in C.H. Chen (Eds.). Pattern Recognition and Signal Processing. Sijhoff & Noordoff. Amsterdam.
Velleman, P.F., & Hoaglin, D.C. (1981). Applications, Basics and Computing of Exploratory Data Analysis. Boston: Duxbury Press.
Winkler, R.L., & Clemen, R.T. (1992). Sensitivity of weights in combining forecasts. Operations Research, 40 (3), 609-614.
Woodward, W.A., Gray, H.L., & Elliott, A.C. (2011). Applied Time Series Analysis. London, U.K.: CRC Press.
Zhang, G.P. (2001). An Investigation of Neural Network Model for Linear Time-Series Forecasting. Computers & Operations Research. 28 (12), 1183-1202.
Zhang, G.P. (2003). Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50, 159-175.
Zhang, G.P., Patuwo, B.E., & Hu, M.Y. (1998). Forecasting with Artificial Neural Networks: The State of the Art. International Journal of Forecasting, 14 (1), 35-62.
Zou, H., & Yang, Y. (2004). Combining time series models for forecasting. International Journal of Forecasting, 20 (1), 69-84.
Zou, H.F., Xia, G.P., Yang, F.T., & Wang, H.Y. (2007). An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting. Neurocomputing, 70 (16), 2913-2923.
The Author wishes to submit the Work to SJM for publication. To enable SJM to publish the Work and to give effect to the parties’ intention set forth herein, they have agreed to cede the first right to publication and republication in the SJM Journal.
Cession
The Author hereby cedes to SJM, who accepts the cession, to the copyright in and to the paper.
The purpose of the cession is to enable SJM to publish the Work, as first publisher world-wide, and for republication in the SJM Journal, and to grant the right to others to publish the Work world-wide, for so long as such copyright subsists;
SJM shall be entitled to edit the work before publication, as it deems fit, subject to the Authors approval
The Author warrants to SJM that:
- the Author is the owner of the copyright in the Work, whether as author or as reassigned from the Author’s employee and that the Author is entitled to cede the copyright to SJM;
- the paper (or any of its part) is not submitted or accepted for publication in any other Journal;
- the Work is an original work created by the Author;
- the Author has not transferred, ceded, or assigned the copyright, or any part thereof, to any third party; or granted any third party a licence or other right to the copyright, which may affect or detract from the rights granted to SJM in terms of this agreement.
The Author hereby indemnifies the SJM as a body and its individual members, to the fullest extent permitted in law, against all or any claims which may arise consequent to the warranties set forth.
No monetary consideration shall be payable by SJM to the Author for the cession, but SJM shall clearly identify the Author as having produced the Work and ensure that due recognition is given to the Author in any publication of the Work.
Should SJM, in its sole discretion, elect not to publish the Work within 1 year after the date of this agreement, the cession shall lapse and be of no further effect. In such event the copyright shall revert to the Author and SJM shall not publish the Work, or any part thereof, without the Author’s prior written consent.