區間型資料一般定義為由一個連續型變數的上限及下限所構成，本文中，我們特別引進了一種與時間相關的區間型資料，在Irpino (2006, Pattern Recognition Letters, 27, 504-513)，他提出每個觀測值皆是由某個時段的起始值及終點值之有方向性的區間所組成，譬如某一支股票在某一周的開盤價和收盤價。過去已經有許多方法運用在區間型資料，但尚未有方法來處理有方向性的區間型資料，然而Irpino 延伸主成分方法來處理有方向性的區間資料。Irpino提出的方法以幾何學的觀點來說，可視為定義在多維度空間上對有方向性線段(一般都稱作“spaghetti”)的分析，在本文中我們有更作進一步的延伸，不僅引入股票的開盤價及收盤價，且引入當周的最高價及最低價來探索Irpino所遺漏的資訊。此外，我們也嘗試用貝他分配來取代Irpino所使用的均勻分配來檢測是否有明顯的改善。延伸的方法需要計算大量複雜的式子，包含了平均數，變異數，共變異數等，最後利用相關係數矩陣進行主成分分析。然而最後的結論為若考慮資訊的價值，以加入最高值和最小值的延伸方法是較好的選擇。 / Interval data are generally defined by the upper and the lower value assumed by a unit for a continuous variable. In this study, we introduce a special type of interval description depending on time. The original idea (Irpino, 2006, Pattern Recognition Letters, 27, 504-513) is that each observation is characterized by an oriented interval of values with a starting and a closing value for each period of observation: for example, the beginning and the closing price of a stock in a week. Several factorial methods have been discovered in order to treat interval data, but not yet for oriented intervals. Irpino presented an extension of principle component analysis to time dependent interval data, or, in general, to oriented intervals. From a geometrical point of view, the proposed approach can be considered as an analysis of oriented segments (nicely called “spaghetti”) defined in a multidimensional space identified by periods. In this paper, we make further extension not only provide the opening and the closing value but also the highest and the lowest value in a week to find out more information that cannot simply obtained from the original idea. Besides, we also use beta distribution to see if there is any improvement corresponding to the original ones. After we make these extensions, many complicated computations should be calculated such as the mean, variance, covariance in order to obtain correlation matrix for PCA. With regard to the value of information, the extended idea with the highest prices and the lowest price is the best choice.

摘要 近幾年發展的區間型態資料之主成份分析，運用在某些領域的資料上尚未成熟，例如股票價格的資料，這些資料是與時間息息相關地，於是有了時間相關的區間資料分析 (Irpino, 2006. Pattern Recognition Letters 27, 504-513)。本文延續這個分析，針對時間相關之區間型台灣股價資料進行研究。Irpino (2006) 的方法只考慮每週的開盤價與收盤價，為了得到更多資訊，我們提出三種方法，第一個方法，將每週的最高價(最低價)納入分析，由兩點的分析變成三點的分析；第二個方法，我們同時考慮最高價與最低價，變成四點的分析，這兩個方法都能得到原始方法不能得到的資訊－公司的穩定度，其中又以第二個方法較為準確；第三種方法引用Irpino (2006) 的建議，我們改變區間的分配，而此方法得到的結果與原 始的方法差異不大。 本文分別收集了台灣金融市場三十家半導體與台指五十中的四十七家公司於民國九十七年九月一號到十二月二十六號共十七週的股價資料進行實證分析。以台指五十為例，分析結果顯示編號17的台達電子工業股份有限公司、編號24的鴻海科技集團，這兩家公司的未來被看好；而編號10的聯陽半導體股份有限公司、編號35的統一超商股份有限公司，此兩家公司的未來不被看好，這四家公司在民國九十八年一月五號到一月七號三天的走勢確實是如此！此外，結果顯示 金融體系的公司比電子體系的公司來得穩定。 關鍵字：主成份分析，區間型資料，時間相關 / ABSTRACT The methods for principal component analysis on interval data have not been ripe yet in some areas, for example, the data of stock prices that are closely related to the time, so the analysis of time dependent interval data was proposed (Irpino, 2006. Pattern Recognition Letters 27, 504-513). In this paper, we apply this approach to the stock prices data in Taiwan. The original “Spaghetti” PCA in Irpino (2006) considered only the starting and the ending prices for each week. In order to get more information we propose three methods. We consider the highest (lowest) price for each week to our analysis in Method 1, and the analysis changes from two points to three points. In Method 2, we consider all information to our analysis which considers four points. These two methods can get more information than the original one. For example, we can get the information of stability degree of the company. For the Method 3, we quote the suggestion from Irpino (2006) to change the distribution of intervals from uniform to beta. However, the result is similar to the original result. In our approach, we collect data of stock prices from 37 companies of semiconductor and 47 companies of TSEC Taiwan 50 index in Taiwan financial market during the 17 weeks from September 1 to December 26, 2008. For TSEC Taiwan 50 index, the results of this analysis are that the future trend of Delta (Delta Electronics Incorporation) which numbers 17 and Foxconn (Foxconn Electronics Incorporation) which numbers 24 are optimistic; And ITE (Integrated Technology Express) which numbers 10 and 7-ELEVEn (President Chain Store Corporation) which numbers 35 are not good. In fact, the trends of these four companies are indicated these results during January 5th to 7th. What’s more, the financial companies are steadier than the electronic industry. Keywords: Principal component analysis; Interval data; Time dependent