Forecasting of time series with trend and seasonal cycle using the airline model and artificial neural networks
Main Article Content
Keywords
prediction, nonlinear macroeconomics, SARIMA, multilayer perceptrons.
Abstract
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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References
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[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.