Time series forecasting by using a neural arima model based on wavelet decomposition

Main Article Content

Eliete Nascimento Pereira
Cassius Tadeu Scarpin
Luíz Albino Teixeira Júnior

Abstract

In the prediction of (stochastic) time series, it has been common to suppose that an individual predictive method – for instance, an Auto-Regressive Integrated Moving Average (ARIMA) model – produces residuals like a white noise process. However, mainly due to the structures of auto-dependence not mapped by a given individual predictive method, this assumption may easily be violated, in practice, as pointed out in Firmino et al. (2015). In order to correct it (and accordingly to produce more forecasts with more accuracy power), this paper puts forward a Wavelet Hybrid Forecaster (WHF) that integrates the following numerical techniques: wavelet decomposition; ARIMA models; Artificial Neural Networks (ANNs); and linear combination of forecasts. Basically, the proposed WHF can map simultaneously linear – by means of a linear combination of ARIMA forecasts – and non-linear – through a linear combination of ANN forecasts – auto-dependence structures exhibited by a given time series. Differently of other hybrid methodologies existing in literature, the WHF forecasts are produced carrying into account implicitly the information from the frequency presenting in the underlying time series by means of the Wavelet Components (WCs) obtained by the wavelet decomposition approach. All numerical results show that WHF method has achieved remarkable accuracy gains, when comparing with other competitive forecasting methods already published in specialized literature, in the prediction of a well-known annual time series of sunspot.

Downloads

Download data is not yet available.

Metrics

Metrics Loading ...

Article Details

Section
Articles
Author Biography

Eliete Nascimento Pereira, Universidade Federal do Paraná

Programa de Pós-graduação em Métodos Numéricos em Engenharia

References

ADHIKARI, R.; AGRAWAL, R. K. (2013) A Homogeneous Ensemble of Artificial Neural Networks for Time Series Forecasting. International Journal of Computer Applications, v. 32, n. 7, p. 8.

BATES, J. M.; GRANGER, C. W. J. (1969) The Combination of ForecastsJournal of the Operational Research Society.

DONOHO, D. L.; JOHNSTONE, J. (1994) M. Ideal spatial adaptation by wavelet shrinkage. Biometrika, v. 81, n. 3, p. 425–455.

FIRMINO, P. R. A.; DE MATTOS NETO, P. S. G.; FERREIRA, T. A. (2015) E. Error modeling approach to improve time series forecasters. Neurocomputing, v. 153, p. 242–254.

HAMILTON, J. D. (1994) Time Series Analysis,1ed. New Jersey : Princeton University Press.

HAVEN, E.; LIU, X.; SHEN, L. (2012) De-noising option prices with the wavelet method. European Journal of Operational Research, v. 222, n. 1, p. 104–112.

HAYKIN, S. S. (2001) Redes Neurais, 2ed. Porto Alegre: Bookman.

KHASHEI, M.; BIJARI, M. A. (2011) New Hybrid Methodology for Nonlinear Time Series Forecasting. Modelling and Simulation in Engineering, v. 2011, p. 1–5.

KUBRUSLY, C. S. (2011) The Elements of Operator Theory, 2 ed. New York: Birkhäuser.

KUBRUSLY, C. S.; LEVAN, N. (2006) Abstract wavelet generated by hilbert space shift operators. Adavances in mathematical Sciences and applications, v. 16, p. 643–660.

LEVAN, N.; KUBRUSLY, C. S. (2003) A wavelet “time-shift-detail” decomposition. Mathematics and Computers in Simulation, v. 63, n. 2, p. 73–78.

LIU, L.-M. (2006) Time Series Analysis and Forecasting. second ed. Chicago, IL: Scientific Computing Associates Corporation.

LUTKEPOHL, H.( 2006) Forecasting with VARMA Models. In: Handbook of Economic Forecasting. [s.l.] Elsevier, v. 1, p. 287–325.

MALLAT, S. (2009) A Wavelet Tour of Signal Processing: The Sparse Way, 3 ed. Burlington: Elsevier Inc.

RAGSDALE, C. (2004) Spreadsheet Modeling & Decision Analysis: A Practical Introduction to Management Science. Fourth edi ed. [s.l.] South-Western.

TEIXEIRA JR, L. A. et al. (2015) Artificial Neural Network and Wavelet decomposition in the Forecast of Global Horizontal Solar Radiation. Sobrapo, v. 35, n. 1, p. 1–16.

ZHANG, G. P. (2003) Time series forecasting using a hybrid ARIMA and neural network model. Neurocomputing, v. 50, p. 159–175.

Similar Articles

You may also start an advanced similarity search for this article.