摘要
關於金融商品價格模型的建立，研究者大多利用時間序列迴歸模型來進行預測分析。此一建模原則，從最早的自我迴歸模型（Autoregressive Model）發展至現今的GARCH 家族，時間序列迴歸模型已發展的非常龐大且複雜。時間序列迴歸模型須建立在定態（stationary）的假設，但財務性時間序列通常都不符合定態的假設，因此需要對原始資料做處理，使之符合假設，或者考慮使用其他方法來分析預測。 本研究利用小波轉換對股價指數做資料前處理，將原始資料分解成許多不同的時間尺度（投資期間）下的小波時間序列，經由小波轉換後所得到的小波時間序列，便成為定態時間序列。繼而針對不同的時間尺度的小波時間序列做訊號延伸，配適最適時間序列模型（小波ARMA 模型）。最後將延伸後的小波時間序列做小波重建，進而得到股價指數的預測序列。本研究分別利用小波ARMA 模型對台灣加權股價指數資料與倫敦黃金現貨價格資料進行建模與預測，並將利用小波ARMA 模型所得到的預測結果與配適ARIMA/GARCH 模型所得模型的預測值做比較。研究結果發現小波ARMA 模型的預測結果優於ARIMA/GARCH模型的預測結果。
並列摘要
Regarding to the model building of financial products, many researchers applied regression method to build time series model for analysis and prediction. The regression model of time series data developed from the earliest Autoregressive model (AR model) to present the GARCH family. The ARIMA/GARCH family has been developed very large and complex. The regression models of time series data have to be built under the data being stationary. Since financial time series data are usually non-stationary, the original data need to be transformed to meet the stationary assumption before model building. Otherwise, other methods to build the finance time series have to be considered. This paper illustrates an application of wavelets as a possible method for prediction of financial data. One of the benefits of a wavelet approach is the flexibility in handling very irregular data series. In this study intended to use wavelet transform to do pre-processing on the finance time series data. The entire procedure can be roughly divided into three steps: wavelet decomposition, signal extension and wavelet reconstruction. The predicted results are compared with output from time series regression model. The most important property of wavelets for economic analysis is decomposition by time scale. Economic and financial systems, like many other systems, contain variables that operate on a variety of time scales simultaneously so that the relationships between variables may well differ across time scales.