本論文主要目的是改善灰色理論在非平滑時間序列的表現，設計不論是在趨勢或非趨勢皆能預測出精準的股價值，特別是針對台灣加權股價指數。趨勢方面利用改良式GM(1,1)進行預測，將背景初始值偏重在近期資料，並利用傅立葉級數與指數平滑法進行一次及二次殘差修正；非趨勢方面，主要利用指標固定區間特色，找出高相關度技術指標，經由模糊時間序列之反模糊化重心法，算出預測的技術指標落點值，並反轉股價取得預測值，再透過隱馬可夫預測出非趨勢區段股價預測值。

利用趨勢與非趨勢系統過往表現，整合兩系統特點，經由支援向量機SVM(Support Vector Machine)分析決策，得到能不論趨勢或非趨勢，皆能獲得良好預測效果系統，最後利用馬可夫模型，找出未來股價可能落在漲跌區間，進而修正出最後的股價預測值，獲得本研究系統預測值。

研究證實，使用改良式GM(1,1)能有效提高傳統GM(1,1)預測，面對市場反轉及隨機性，能獲得顯著提升與改善，而使用技術指標進行模糊時間序列，搭配隱馬可夫模型，則能有效找到非趨勢市場轉折點。整合兩套系統進行判別，能達到無論是趨勢或非趨勢皆能穩定預測。

The main purpose of this study is to improve the performance of grey theory in non-smooth time series, so that after modification, the theory can predict stock value more accurate both in the trend or non-trend, especially Taiwan’s weighted share price index. In the trend, we use the modified GM (1,1) in which the initial value of the background is set in the near-term data, and use the Fourier series and exponential smoothing method to perform primary and secondary residual correction. In the non-trend, we mainly use the fixed range characteristics to find out the technical index of high relevance. Through the predicted technical index placement value predicted by the fuzzy time series of defuzzification center of gravity method, we reverse the stock value. Finally, through the hidden Markov forecast non-trend segment value, we predict actual forecast stocks.

Through analysis and decision-making process provided by the support vector machine, grey theory integrated the advantages of both trend and non-trend system and will be able to work effectively in terms of stock value prediction. The use of Markov model helps to find out in which section stock prices may fall, correct the real final stock price forecast, and obtain the value of system prediction.

It is proved that the modified GM (1,1) can effectively improve the traditional GM (1,1) prediction when faced with market reversal and randomness. Combined with the hidden Markov model, the use of technical index conducting fuzzy time series can effectively find non-trend market turning point. The integration of modified GM (1,1) and technical index systems makes more accurate predictions in both trend and non-trend.

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