在時間序列模式的預測上，經常使用指數加權移動平均(EWMA)的方法來調整預測誤差，降低因趨勢出現了結構性變化所產生的趨勢變異，使預測模式能得到較佳的預測結果。過去的研究已提出了廣泛加權移動平均(GWMA)的方法及概念，證實了它的概念與EWMA方法相同，但是GWMA方法多了一個參數，在偵測小偏移變動時較為敏感，應用的範圍也較EWMA廣泛。因此，本論文應用GWMA的概念及方法，導入在追踪信號的狀態空間模式中的限制式的衰減趨勢(restricted damped trend)模式，將結構性變化所導致的平滑誤差統計量，由EWMA形式改變成GWMA形式，使預測模式增加一項調整參數λ，將模式區分成λ<1、λ=1及λ>1三種情況，λ=1時為原來的限制式衰減趨勢模式，另外多增加了λ<1及λ>1的情況，使模式的適用範圍更為廣泛，並針對各項參數值對預測模式所產生的影響進行比較，找出此GWMA預測模式較佳的參數值設定範圍。

而在預測的領域中，除了應用於企業營運績效及財務的預測外，最常應用的領域非金融市場莫屬，尤其是在股票市場的股價指數及外匯市場的匯率變動的預測。由於全球化趨勢使得國際金融交易的波動性及關連性增加，國際股市的漲跌都或多或少會影響他國的股票市場，尤其是美國DJ工業指數在國際股市都扮演一個極重要的角色，過去的研究皆以美國股市來作為各種預測模式的因子，進行他國股價指數之預測。而這些探討國際間金融市場連動關係所進行的預測模式又常使用EWMA方法，因此，本論文亦提出以GWMA方法應用於金融市場預測領域，以取代過去常用的EWMA方法，結合美國DJ工業指數、NASDAQ指數、日經NI225指數、韓國KOSPI指數、及香港HSI指數等多個國際股價指數的波動組合來預測台灣加權股價收盤指數，找出最小預測誤差的國際股市組合以及最佳組合的GWMA模式的參數設定值，並與EWMA模式做比較，探討兩種預測模式之差異。

關鍵詞：指數加權移動平均; 廣泛加權移動平均; 追蹤訊號; 預測; 多國股價指數

Time series models often use the exponentially weighted moving average (EWMA) method to adjust the prediction error and reduce structural changes arising from variations in trends, enabling the model to obtain better forecasting results. In past research, had proposed the generally weighted moving average (GWMA) method and proved that this method is almost identical to the EWMA method. The GWMA method adds a parameter, is more sensitive to small fluctuations, and has a wider range of applications than EWMA. Therefore, this dissertation applies the GWMA method to a restricted damped trend model that changes the smoothed error statistic from the EWMA form to the GWMA form, and adds a correction parameter to distinguish three scenarios: , , and . The original restricted damped trend model applies only to , enabling the model to capture situations in which and , increasing its generality. This dissertation also compares the effect of various parameter values on the predictive model and finds the range of parameter settings that optimize the model.

In addition to forecasting of a company's operating performance, the most applicable field for this model is the financial markets, in particular predicting changes in these markets, stock indexes, and exchange rates. Globalization has increased the volatility of international financial transactions, particularly those related to the international stock markets. An increase in the volatility of one country’s stock market spreads throughout the globe, affecting other countries’ stock markets. In particular, the Dow Jones Industrial Average plays an extremely important role in the international stock market. Past studies used this American stock market as a factor in various models to predict the performance of other countries’ stock indexes. These studies explored national index-linked relationship forecasting models, which were often based on the EWMA method. This study replaces the EWMA method with the GWMA method in the forecasting field and data from the Dow Jones Industrial Average, the NASDAQ, Japan’s Nikkei 225, the Korea Composite Stock Price Index, and the Hong Kong Hang Seng Index to predict the performance of the Taiwan Capitalization Weighted Stock Index. This study attempts to find the smallest prediction error using the optimal combination of GWMA model parameters and various international stock market data, and compares the results with that found using the EWMA model to explore differences between the two types of forecasting models.

Keywords：EWMA; GWMA; Tracking signal; Forecasting; multi-stock index

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