| In this thesis, we develop a new forecasting method by merging traditional statistical methods with innovational non-statistical theories for the purpose of improving prediction accuracy of stock time series. The method is based on a novel hybrid model which combines the grey model, the ARIMA model and wavelet methods. First of all, we improve the traditional GM(1, 1) model to the GM(1, 1, mu, upsilon) model by introducing two parameters: the grey coefficient and the grey dimension degree upsilon. Then we revise the normal G-ARMA model by merging the ARMA model with the GM(1, 1, mu, upsilon) model. In order to overcome the drawback of directly modeling original stock time series, we introduce wavelet methods into the revised G-ARMA model and name this new hybrid model WG-ARMA model. Finally, we obtain the WPG-ARMA model by replacing the wavelet transform with the wavelet packet decomposition. To keep consistency, all the proposed models are merged into a single model by estimating-parameters simultaneously based on the total absolute error (TAE) criterion. To verify prediction performance of the models, we present case studies for the models based on the leading Canadian stock index: S&P/TSX Composite Index on the daily bases. The experimental results give the rank of predictive ability in terms of the TAE, MPAE and DIR metrics as following: WPG-ARMA, WG-ARMA, G-ARMA, GM(1, 1, mu, upsilon), ARIMA. |
