Forecasting of time series with trend and seasonal cycle using the airline model and artificial neural networks

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J D Velásquez
C J Franco


prediction, nonlinear macroeconomics, SARIMA, multilayer perceptrons.


Many time series with trend and seasonal pattern are successfully modeled and forecasted by the airline model of Box and Jenkins; however, this model neglects the presence of nonlinearity on data. In this paper, we propose a new nonlinear version of the airline model; for this, we replace the moving average linear component by a multilayer perceptron neural network. The proposed
model is used for forecasting two benchmark time series; we found that theproposed model is able to forecast the time series with more accuracy that other traditional approaches.

MSC: 62M10, 62M20


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[1] GEP. Box, GM. Jenkins. Time Series Analysis: Forecasting and Control. Holden–Day Inc, 1970

[2] D. van Djck. Smooth Transition Models: Extensions and Outlier Robust Inference. PhD thesis, Erasmus University - Rotterdam, 1999. Referenciado en 173

[3] C. Granger, T. Terasvirta. Modeling Nonlinear Economic Relationships. Oxford University Press, 1993.

[4] I. Kaastra, M. Boyd. Designing a neural network for forecasting financial and economic series. Neurocomputing 10: 215–236, 1996.

[5] GP. Zhang, B. Patuwo, M. Hu. Forecasting with artificial neural networks: the state of the art. International Journal of Forecasting, 14: 35–62, 1998.

[6] MC. Medeiros, C. Veiga. A hybrid linear-neural model for time series forecasting. IEEE Transactions on Neural Networks, 11(6): 1402–1412, 2000.

[7] MC.Medeiros, A. Veiga. A flexible coefficient smooth transition time series model. IEEE Transactions on Neural Networks, 16(1): 97–113, 2005.

[8] G. Inoussa, H. Peng, J. Wu. Nonlinear time series modeling and prediction using functional weights wavelet neural network-based state-dependent AR model. Neurocomputing, 86(1): 59–74, 2012.

[9] EWM Lee, RKK. Yuen, SM. Lo, KC. Lam, GH. Yeoh. A novel artificial neural network fire model for prediction of thermal interface location in single compartment fire. Fire Safety Journal, 39(1): 67–87, 2004.

[10] B. Pang, S. Guo, L. Xiong, L. Chaoqun. A nonlinear perturbation model based on artificial neural network. Journal of Hydrology, 222(2-4): 504–516, 2007.

[11] R. Hassan, B. Nath, M. Kirley. A fusion model of HMM, ANN and GA for stock market forecasting. Expert Systems with Applications, 33(1): 171–180, 2007.

[12] TL. Lai, SPS. Wong. Stochastic neural networks with applications to nonlinear time series. Journal of the American Statistical Association, 96(455): 968–981, 2001.

[13] Y, Chen, B. Yang, J. Dong, A. Abraham. Time-series forecasting using flexible neural tree model. Information Sciences, 174(3-4): 219–235, 2005.

[14] M. Ghiassi, H. Saidane. A dynamic architecture for artificial neural networks. Neurocomputing, 63: 397–413, 2005.

[15] M. Suarez-Farinas, CE. Pedreira, MC. Medeiros. Local global neural networks: a new approach for nonlinear time series modeling. Journal of the American Statistical Association, 99(468): 1092–1107, 2004.

[16] WK. Wong, M. Xia, WC. Chu. Adaptive neural network model for time-series forecasting. European Journal of Operational Research, 207(2): 807–816, 2010.

[17] GP. Zhang. Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, 50: 159–175, 2003.

[18] CH. Aladag, E. Egrioglu, C. Kadilar. Forecasting nonlinear time series with a hybrid methodology. Applied Mathematics Letters, 22(9): 1467–1470, 2009.

[19] F-M. Tseng, H-C. Yu, GH. Tzeng. Combining neural network model with seasonal time series ARIMA model. Technological Forecasting and Social Change, 69(1): 71–87, 2002.

[20] L. Yu, S. Wang, KK. Lai. A novel nonlinear ensemble forecasting model incorporating GLAR and ANN for foreign exchange rates. Computers & Operations
Research, 32(10): 2523–2541, 2005.

[21] HF. Zou, GP. Xia, FT. Yang, HY. Wang. An investigation and comparison of artificial neural network and time series models for Chinese food grain price forecasting. Neurocomputing, 70(16-18): 2913–2923, 2007.

[22] M. Khashei, M. Bijari. An artificial neural network (p, d, q) model for time series forecasting. Expert Systems with Applications, 37(1): 479–489, 2010.

[23] M. Khashei, M. Bijari. A novel hybridization of artificial neural networks and ARIMA models for time series forecasting. Applied Soft Computing, 11(2): 2664– 2675, 2011.

[24] N. Kasabov. Foundations of Neural Networks, Fuzzy Systems, and Knowledge Engineering. 2nd edition. Massachusetts Institute of Technology, 1998.

[25] W. Sarle. Neural networks and statistical models. Proceedings of the 19th Annual SAS Users Group Int. Conference, 1538–1550, 1994.

[26] T. Masters. Practical Neural Network Recipes in C++. First edn, Academic Press, Inc, 1993.

[27] T. Masters. Neural, Novel and Hybrid Algorithms for Time Series Prediction. First edn, John Wiley and Sons, Inc., 1995.

[28] GP. Zhang. An investigation of neural networks for linear time-series forecasting. Computers & Operations Research, 28(12): 1183–1202, 2001.

[29] M. Nelson, T. Hill, W. Remus, and M. O’Connor. Time series forecasting using neural networks: should the data be deseasonalized first? Journal of Forecasting, 18: 359–367, 1999.

[30] GP. Zhang, M. Qi. Neural network forecasting for seasonal and trend time series. European Journal of Operational Research, 160(2): 501–514, 2005.

[31] J. Faraway, C. Chatfield. Time series forecasting with neural networks: A comparative study using the airline data. Applied Statistics, 47(2): 231–250, 1998.

[32] R. McCleary, RA. Hay, Jr. Applied time series analysis for the social sciences. Sage Publications, London, 1980.