不同時間間距下，核密度帶寬估計對於時間序列相關性的影響：以臺積電與聯電的股價與成交量為例

Abstract

若將個股成交量定義成「事件」性質的變數，則從事件的角度而言，在單一的時間點可能沒有發生，也可能發生了很多次。而且當這樣的事件變數有兩個以上時，兩事件之間也很有可能具有時間上的延遲反應。因此若要研究其之間真實的相關性，以固定的時間間距(time span)整合資料、以核密度估計(KDE)取得較理想的密度呈現、多元時間序列分析等方法或可進行嘗試。 本文使用臺灣證券交易所官網上，臺積電與聯電十年(2009~2018)的股票與成交量日資料。透過相關係數拔靴法信賴區間與T檢定選出合適的核密度估計帶寬(bandwidth)與時間間距，以此建立多種情境組合並進行VARIMA模型配適。結論發現使用核密度估計或是時間間距皆可以使變項之間的相關性更為接近真實情形，後續的VARIMA模型建置也會有更好的模型解釋力。同時在所有情境組合中，VARIMA(1,1,2)模型具有最佳的解釋力，因此其可作為以此二家公司股票進行配對交易時的策略參考。

If stock volumes are defined by “event”, they may happen many times or not to happen in one single time point at the aspect of event. Also, when there are two or more event variables like that in the dataset, the reaction of delay will probably happen between them. Therefore, if we want to figure out the true correlation between each two of them, methods like using same time span to integrate data, using kernel density estimation (KDE) to gain optimal density, or multivariate time series analysis can be used to try and test. Dataset of this study is the ten year (2009~2018) daily price and volume data of TSMC (Taiwan Semiconductor Manufacturing Company, Limited) and UMC (United Microelectronics Corporation), retrieved from the official website of Taiwan Stock Exchange. By using correlation bootstrap confidence intervals and T-tests, the study can select the appropriate bandwidths and time spans. After that, the study constructs different situations of data transformation by the former result, and fit VARIMA models in each situation. In conclusion, using KDE or time span can both make correlations of variables closer to the real, and the following VARIMA model can have better explanation. Meanwhile, VARIMA(1,1,2) model explained the best among all the situations in this empirical research, so it can be a reference of pairs trading strategies of the two companies.