To improve time series forecasts the wavelet decomposition has been applied. The combination of forecasting methods as the Autoregressive Integrated Moving Average (ARIMA) and Artificial Neural Networks have been used to achieve a higher quality time series forecasting than. This paper proposed a hybrid model composed of wavelet decomposition, ARIMA and neural network Multilayer Perceptron. These models are combined linearly then yielding the time series forecasting. The series studied are the Wolf's sunspots and the British pound/US dollar exchange rate data. The comparison of the proposed model in this paper with literature indicated an effective way to improve forecasting. 7432Eliete Nascimento Pereira et al.

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 might be easily violated, in practice, as pointed out by Firmino et al. (2015). In order to correct it