An Interactive Wavelet Artificial Neural Network in Time Series Prediction

An interactive mathematical methodology for time series prediction that integrates wavelet de-noising and decomposition with an Artificial Neural Network (ANN) method is put forward here. In this methodology, the underlying time series is initially decomposed into trend and noise components by a wavelet de-noising method. Both trend and noise components are then further decomposed by a wavelet decomposition algorithm generating Wavelet Components (WCs) for each one. Each WC is individually modeled by an ANN method in order to produce both in-sample and out-of-sample (point) forecasts. At each time t, the forecasts of the WCs of the trend and noise components are added to provide in-sample and out-of-sample forecasts of the underlying time series. This methodology, applied to the well-known Canadian lynx time series that, as pointed by [1], exhibit non-linear and non-Gaussian characteristics, is shown to outperform other methods traditionally applied to this data.