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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