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

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