In this thesis, we revised and proposed several models and then used them to forecast the stock index. The first model is an improved version of the GM (1, 1) model by introducing two parameters. Then we revised the normal hybrid model G-ARMA by merging the ARMA model with the improved GM (1, 1) model. In order to overcome the drawback of directly modeling original stock index, we introduced wavelet methods into the revised G-ARMA model and named this new hybrid model WG-ARMA. Finally, we obtained the last hybrid model WPG-ARMA by replacing the wavelet transform with the wavelet packet decomposition. For hybrid models, we estimated parameters of the hybrid models as the whole instead of estimating parameters for each sub-model separately. To verify prediction performance of the models, we presented case studies for the models based on a leading Canadian stock index. The experimental results gave the rank of predictive ability in terms of the TAE, MPAE and DIR metrics as following: WPG-ARMA model, WG-ARMA model, revised G-ARMA model, improved GM (1, 1) model, and ARIMA model.

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