利用上證綜合指數和台灣證券交易所發行量加權股票指數的月資料，本論文解決指數和股票的關聯問題。找到這個關聯有兩個問題。第一個問題是機率統計方法需要巨大的數據來解決大樣本多重數據的不確定性。另一個問題是，股票數據量太大，影響了我們使用它的能力。為了解決這兩個問題，我們建構了一個數據庫，以減少股票數據的規模，並使用鄧聚龍教授(1982 and 1989a,b)所建立的灰色系統(Grey System)技術理論，為衡量指數與股票之間的關聯提供了框架。這些發現可能為投資者做出投資決策提供了足夠的參考。
本文提供了五個主要發現。首先，TAIEX中的成分權重值與關係係數序列沒有灰色正相關。第二，上海綜合指數的成分權重值與關係係數也沒有灰色正相關。第三，與TAIEX最相關的股票是南亞塑料，它可以被認為TAIEX的同等指標。第四，與上海綜合指數最相關的股票是交通銀行，可以作為上海綜合指數的同等指標。最後，在兩個不同的市場中，跟指數有最高相關性的股票很巧合都排名第八，結果與許多投資者使用的經驗法則沒有太大的驚訝。

Using monthly data of Shanghai Composite index and the Taiwan Stock Exchange Capitalization Weighted Stock Index, this paper solves the association problem of index and stocks. To find the association has two problems. The first problem is that probability statistical methods require huge data to solve uncertainties from large sample multiple data. The other problem is that the volume of stock data is so large that it affects our ability to use it. To solve these two problems, we constructed a database to reduce the size of stock data and used technical theory of gray system developed by Deng (1982 and 1989a,b) that provides a framework to measure the association between index and stocks. These findings may provide investors with enough reference to make investment decision.
This paper provides five major findings. First, the weighting value of constituents in TAIEX was not positively gray-correlated with the relational coefficient sequence. Second, the weighting value of constituents in Shanghai Composite index was not positively gray-correlated with the relational coefficient sequence, too. Third, the stock most strongly correlated with TAIEX was Nan-Ya Plastics, and it can be regarded as a coincident indicator of TAIEX. Fourth, the stock most strongly correlated with Shanghai Composite index was Bank of Communications, and it can be regarded as a coincident indicator of Shanghai Composite index. Finally, in two different markets, stocks with the highest correlation with the index are coincidentally ranked eighth, and the results didn't surprise substantially from the rules of thumb used by many investors.

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