Disaggregation & aggregation of time series components: A hybrid forecasting approach using generalized regression neural networks and the theta method

A hybrid forecasting method is proposed which leverages from statistical and neural network techniques to perform multi-step ahead forecasting. The proposed method is based on the disaggregation of time series components, the prediction of each component individually and the reassembling of the extrapolations to obtain an estimation for the global data. The STL decomposition procedure from the literature [5] is implemented to obtain the seasonal, trend and irregular components of the time series, whilst Generalized Regression Neural Networks (GRNN) [12] are used to perform out-of sample extrapolations of the seasonal and residual components. The univariate Theta model is employed for the estimation of the directional component. The application of the GRNN is based on the dynamic calibration of the training process for each of the seasonal and irregular components individually. The proposed hybrid forecasting method is applied to 60 time series from the NN3 competition and 227 time series from the M1 Competition dataset, to obtain 18 out-of sample predictions. The results from the application demonstrate that the proposed method can outperform standard statistical techniques in the literature. One of the main contributions of the current research lies in the investigation of the strengths and weaknesses of the GRNN in extrapolating structural components of time series.

[1]  Stephen A. Billings,et al.  On-line Supervised Adaptive Training Using Radial Basis Function Networks , 1996, Neural Networks.

[2]  Selwyn Piramuthu,et al.  Using Feature Construction to Improve the Performance of Neural Networks , 1998 .

[3]  Michael Y. Hu,et al.  Forecasting with artificial neural networks: The state of the art , 1997 .

[4]  Steven C. Hillmer,et al.  Issues Involved With the Seasonal Adjustment of Economic Time Series , 1984 .

[5]  J. Ord,et al.  A New Look at Models For Exponential Smoothing , 2001 .

[6]  Marina Theodosiou,et al.  Forecasting monthly and quarterly time series using STL decomposition , 2011 .

[7]  K. Wallis.  Seasonal Adjustment and Relations Between Variables , 1974 .

[8]  Spyros Makridakis,et al.  The M3-Competition: results, conclusions and implications , 2000 .

[9]  Robert Fildes,et al.  Generalising about univariate forecasting methods: Further empirical evidence , 1998 .

[10]  E. S. Gardner,et al.  Seasonal exponential smoothing with damped trends , 1989 .

[11]  An-Sing Chen,et al.  Forecasting Exchange Rates Using General Regression Neural Networks , 1999, Comput. Oper. Res..

[12]  E. Michael Azoff,et al.  Neural Network Time Series: Forecasting of Financial Markets , 1994 .

[13]  Germano C. Vasconcelos,et al.  A systematic solution for the NN3 Forecasting Competition problem based on an ensemble of MLP neural networks , 2008, 2008 19th International Conference on Pattern Recognition.

[14]  M. Medeiros,et al.  Linear models, smooth transition autoregressions, and neural networks for forecasting macroeconomic time series: A re-examination , 2005 .

[15]  Ulrich Anders,et al.  Model selection in neural networks , 1999, Neural Networks.

[16]  Marie Cottrell,et al.  Neural modeling for time series: A statistical stepwise method for weight elimination , 1995, IEEE Trans. Neural Networks.

[17]  Fang-Mei Tseng,et al.  Combining neural network model with seasonal time series ARIMA model , 2002 .

[18]  A. Refenes.  Neural Networks in the Capital Markets , 1994 .

[19]  Christopher A. Sims,et al.  Seasonality in Regression , 1974 .

[20]  Paul Newbold,et al.  Structural decomposition of time series with implications in economics, accounting, and finance research , 1991 .

[21]  Hikmet Kerem Cigizoglu,et al.  Generalized regression neural network in monthly flow forecasting , 2005 .

[22]  Simon Haykin,et al.  Neural Networks: A Comprehensive Foundation , 1998 .

[23]  C. Holt.  Author's retrospective on ‘Forecasting seasonals and trends by exponentially weighted moving averages’ , 2004 .

[24]  Jung-Hua Wang,et al.  Stock market trend prediction using ARIMA-based neural networks , 1996, Proceedings of International Conference on Neural Networks (ICNN'96).

[25]  Thomas Kolarik,et al.  Time series forecasting using neural networks , 1994, APL '94.

[26]  Victor L. Berardi,et al.  Time series forecasting with neural network ensembles: an application for exchange rate prediction , 2001, J. Oper. Res. Soc..

[27]  Chris Chatfield,et al.  Time series forecasting with neural networks: a comparative study using the air line data , 2008 .

[28]  Guoqiang Peter Zhang,et al.  Neural network forecasting for seasonal and trend time series , 2005, Eur. J. Oper. Res..

[29]  Edward Gately.  Neural networks for financial forecasting , 1995 .

[30]  Donald F. Specht,et al.  A general regression neural network , 1991, IEEE Trans. Neural Networks.

[31]  Robert L. Winkler,et al.  The accuracy of extrapolation (time series) methods: Results of a forecasting competition , 1982 .

[32]  J. V. Hansen,et al.  Forecasting and recombining time-series components by using neural networks , 2003, J. Oper. Res. Soc..

[33]  Allan Timmermann,et al.  On the optimality of adaptive expectations: Muth revisited , 1995 .

[34]  Christopher M. Bishop,et al.  Neural networks for pattern recognition , 1995 .

[35]  Rob J Hyndman,et al.  Prediction Intervals for Exponential Smoothing State Space Models , 2001 .

[36]  Irma J. Terpenning,et al.  STL : A Seasonal-Trend Decomposition Procedure Based on Loess , 1990 .

[37]  William Remus,et al.  Neural Network Models for Time Series Forecasts , 1996 .

[38]  Saeed Heravi,et al.  Linear versus neural network forecasts for European industrial production series , 2004 .

[39]  S.F. Crone,,et al.  Stepwise Selection of Artificial Neural Network Models for Time Series Prediction , 2005 .

[40]  Chao Ton Su,et al.  Combining time series and neural network approaches for modeling reliability growth , 1997 .

[41]  Spyros Makridakis,et al.  Forecasting Methods for Management , 1989 .

[42]  Guoqiang Peter Zhang,et al.  Time series forecasting using a hybrid ARIMA and neural network model , 2003, Neurocomputing.

[43]  Chunhang Chen,et al.  Robustness properties of some forecasting methods for seasonal time series: A Monte Carlo study☆ , 1997 .

[44]  Philip D. Wasserman,et al.  Advanced methods in neural computing , 1993, VNR computer library.

[45]  Rob J Hyndman,et al.  Prediction intervals for exponential smoothing using two new classes of state space models 30 January 2003 , 2003 .

[46]  Peter R. Winters,et al.  Forecasting Sales by Exponentially Weighted Moving Averages , 1960 .

[47]  Everette S. Gardner,et al.  Exponential smoothing in the telecommunications data , 2008 .

[48]  Suhartono Suhartono,et al.  THE EFFECT OF DECOMPOSITION METHOD AS DATA PREPROCESSING ON NEURAL NETWORKS MODEL FOR FORECASTING TREND AND SEASONAL TIME SERIES , 2007 .

[49]  K. Nikolopoulos,et al.  The theta model: a decomposition approach to forecasting , 2000 .

[50]  Apostolos Nikolaos Refenes,et al.  Stock ranking: neural networks vs multiple linear regression , 1993, IEEE International Conference on Neural Networks.

[51]  Rob J Hyndman,et al.  Unmasking the Theta Method , 2003 .

[52]  Rob J Hyndman,et al.  Automatic Time Series Forecasting: The forecast Package for R , 2008 .

[53]  William Remus,et al.  Time series forecasting using neural networks: should the data be deseasonalized first? , 1999 .

[54]  C. Chatfield,et al.  Neural networks: Forecasting breakthrough or passing fad? , 1993 .

[55]  Rob J Hyndman,et al.  A state space framework for automatic forecasting using exponential smoothing methods , 2002 .