本文選取樣本包括上海與深圳A、B股指數，資料時間起點為西元1997年1月1日至2001年9月30日止，各1146筆資料。結論如下：（一）以BDS統計量發現大陸證券A、B股（包括上海與深圳股價指數與報酬數列）並不符合獨立一致性分配（I.I.D），拒絕隨機漫步之假設。（二）以ARMA（1, 0）模型配適後所得之殘差數列進行BDS統計檢定能拒絕I.I.D.之需無假設，故顯示報酬數列具非線性波動之特性，故再以R/S分析法加以確認非線性現象的存在與否。（三）以R/S分析法發現：不管以Hurst指數法或天花圖法均得到H值均大於0.5的相同結果，代表各指數樣本符合非線性之假設，且為正向趨勢性數列，因此不符合效率市場假說。（四）以相關維度分析發現，上海與深圳A、B股指數報酬數列於證監會宣布休市前、後都不具有混沌現象，屬於隨機系統，屬於隨機過程而非確定過程。（五）以GARCH模型配適結果發現，AR（1）- GARCH（1,1）模型最適用於解釋大陸證券A、B股市場之波動性。且各樣本之αi＋βi係數值顯著趨近於1顯示大陸證券A、B股市場之報酬波動具有持續性。上海與深圳A、B股AR（1）- GARCH（1﹐1）模型殘差的經ARCH-LM測試顯示各樣本殘差項並沒有明顯的條件異質性變異性，所以可以推論本研究之樣本--上海與深圳A、B股指數報酬數列資料可能為混沌現象或非線性結構。（六）GARCH-M模型顯示，上海A股股價報酬數列之條件變異數項（θ）係數在5﹪下顯著；深圳B股股價報酬數列之條件變異數項（θ）係數在10﹪下顯著，顯示此二市場的條件波動對預期報酬有影響。深圳A股與上海B股股價報酬數列條件變異數項（θ）係數並不顯著，可知此二市場條件波動對預期報酬之影響並不存在，不同時點的波動性並不會影響到此二新興市場之報酬。 關鍵字：BDS統計量、R/S分析法、相關維度分析、GARCH族模型 This study examines the chaos and volatility of China daily stock indexes, including Shanghai and Shenzhen A and B Stock Markets. Three techniques i.e. BDS Test, Rescale Range Analysis, Correlation Dimension Analysis are applied to detect chaotic behavior in this research. We use these techniques to analyze four categories of China listed stocks for the period form January 1, 1997 to September 30, 2001. The BDS statistics of four return series imply the rejection of the hypothesis of independent, identical distribution (I.I.D.).The Correlation Dimensions are not convergent that tell us there are not obviously evidence chaotic behavior be presented in the four stock indexes return . Four H values for Rescale Range Analysis are quite greater than 0.5, it indicates that the time series is probably persistent (long memory). The results of this approach might provide us with a better understanding of China stock market. Although the linear dependence is excluded from the returns series by fitting ARMA model, the phenomena of non-linearity is present. Therefore, GARCH models are employed to capture the non-linearity embedded in the return series. We find significant existence of volatility from the results of GARCH models. In order to examine the relation between risk and expected return, in addition, GARCH-M models are chosen and show no significant evidence on the coefficient of conditional volatility in Chinese B stock market.
