在股票市場中，股價的表現與市場資訊息息相關。例如美國在2007 年爆發的次級房貸危機影響了全球的金融市場，全球股市也紛紛受到影響，而在美國聯邦準備理事會採取一連串的處理措施之後，市場才逐漸平穩下來。可見交易大眾對新進市場資訊的反應會造成各式各樣的股價走勢，因此股價時間序列資料的樣式比對對於未來股價走勢的預測、規則發現以及利用電腦進行分析調查而言是一個重要的課題。在本篇研究當中，我們提出一套樣式比對的流程有助於尋找兩家上市公司同日的股價有相同表現的時間區段。首先我們利用最長共同子序列的演算法篩選出這兩家公司平均市場累積波動與股價漲跌相似的時段，再將相似時段的股價資料轉換為保力加通道百分比的資料，並利用光譜分析以及卡方檢定研判這些配對時段在接收到相同的市場資訊後，股價的走勢與波動是否相似。我們先以模擬探討此樣式比對流程的適用性並且將方法應用在紐約證券交易所的高頻交易資料分析。

In security markets, the stock price movements are closely linked to the market information. For example, the subprime mortgage triggered a global financial crisis in 2007. Drops occurred in virtually every stock market in the world. After the Federal Reserve took several steps to address the crisis, the stock markets have been gradually stable. Reaction of the traders to the arrival information results in different patterns of the stock price movements. Thus pattern matching is an important subject in future movement prediction, rule discovery and computer aided diagnosis. In this research, we propose a pattern matching procedure to seize the similar stock price movements of two listed companies during one day. First, the algorithm of searching the longest common subsequence is introduced to sieve out the time intervals where the two listed companies have the same integrated volatility levels and price rise/drop trends. Next we transform the raw price data in the found matching time periods to the Bollinger Band Percent data, then use the power spectrum to extract low frequency components. Adjusted Pearson chi-squared tests are performed to analyze the similarity of the price movement patterns in these periods. We perform the study by simulation investigation first, then apply the procedure to empirical analysis of high frequency transaction data of NYSE.

1 Introduction 1
2 Methodologies 2
2.1 Longest Common Subsequence 2
2.2 Bollinger Band Percent 4
2.3 Piecewise Linear Representation 6
2.4 The Power Spectrum 8
3 Pattern Matching in Simulation Data 10
3.1 Data Generating Process 10
3.2 Application of the LCS Method to Financial Data 12
3.3 Price Pattern Matching Using the PLR 13
3.4 Price Pattern Matching Using the Power Spectrum of %b 15
4 Empirical Study 18
5 Conclusion 20
Appendix 21
Appendix A 21
Appendix B 22
Appendix C 23
References 30

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