本研究以跳躍擴散模型(GARCH-JD)及Chan and Maheu(2002)的ARJI模型，探討資產報酬為SGED分配下，美國及金磚四國(巴西、俄羅斯、印度及中國；BRICs)等五個國家之股價指數日報酬率是否存在跳躍的現象與是否具備高峰、厚尾及波動叢聚等特性，並以概似比率檢定檢驗模型的配適性，最後再分析模型在成熟市場與新興市場上，對於統計特性捕捉能力的優劣性。
實證結果發現這五個國家的條件報酬分配普遍存在高狹峰及波動叢聚的現象，但俄羅斯在GARCH-JD及ARJI模型上及中國在GARCH-JD模型上無法捕捉到偏態特性。跳躍分析過程中，發現除了巴西之外，均能捕捉到顯著的跳躍現象，跳躍過程具備了與時俱變的特徵，跳躍參數中觀察到各國股價的波動有必要考量跳躍的現象，當資產報酬設定為SGED分配時，在捕捉統計特性上更具效率。ARJI模型在SGED分配假設下發現成熟市場在消化前期對於當期股價報酬率的影響是較具效率的，但前期不可預期的價格波動對於成熟市場當期的影響卻較新興市場來得強烈。最後從概似比率檢定觀察到所有國家使用SGED模型來估計的結果均較常態分配的模型有顯著的配適度，整體而言，ARJI模型捕捉統計特性的能力優於GARCH-JD模型，且ARJI模型運用於新興市場較之運用於成熟市場有更好的解釋能力。

This paper adopts the GARCH jump model and ARJI model of Chan and Maheu(2002) that combine the skewed generalized error distribution of asset returns, in order to examine the jump, leptokurtosis and volatility clustering for the rates of returns of America and BRICs. We also employ likelihood ratio test for testing goodness of different models. In conclusion, we analyze different models’ capture ability for statistic features of mature market and emerging markets.
The empirical results indicated that the five countries exist heavy tail and volatility clustering, but GARCH-JD and ARJI model with Russia and GARCH-JD with China can’t capture skewness. We also find these countries’ stock returns except Brazil with the two models have significant characteristic of jumping and jump process is provided with time varying. It’s better efficient when we assume that asset returns obey SGED. The ARJI model with SGED of asset returns develop that the diminishing efficiency for mature markets is faster then emerging markets while the earlier stage’s returns affect it at present. But mature markets’ nonpredictive volatility in early days for effecting upon at once is stronger then emerging markets. In the end, the likelihood ratio test demonstrate that these countries using SGED have more significant goodness of fit then using normal distribution. Totally, the ARJI model captures statistical property’s ability surpasses the GARCH-JD model and the ARJI model utilizes to the emerging markets compared with utilizes has the better explanation ability to the mature market.

目  錄
第壹章　緒論………………………………………………………	1
第一節　研究背景與動機………………………………………	1
第二節　研究目的………………………………………………	3
第三節　研究架構………………………………………………	5

第貳章　相關理論與文獻回顧……………………………………	6
第一節　相關理論………………………………………………	6
第二節　國內外文獻回顧………………………………………	8

第參章　研究方法…………………………………………………11
第一節　單根檢定…………………………………………………11
第二節　ARCH檢定…………………………………………………16
第三節　GED分配………………………………………………… 19
第四節　GARCH(1,1)模型…………………………………………22
第五節　GARCH-JD模型……………………………………………24
第六節　ARJI模型…………………………………………………26
第七節　ARJI-SGED模型………………………………………… 29
第八節　概似比率檢定……………………………………………32

第肆章　實證分析…………………………………………………33
第一節　資料來源整理……………………………………………33
第二節　基本統計特性分析………………………………………36
第三節　單根檢定…………………………………………………37
第四節　ARCH檢定…………………………………………………43
第五節　實證結果分析……………………………………………44

第伍章　結論………………………………………………………52
	
參考文獻……………………………………………………………55


表  次
【表3.1】SGT家族機率密度函數表………………………………21
【表4.1】各國家股價指數報酬率基本統計量………………… 36
【表4.2】各國家股價指數報酬率選取最適落階期準則……… 38
【表4.3】各國家股價指數報酬率ADF單根檢定(水準項)………40
【表4.4】各國家股價指數報酬率ADF單根檢定(差分項)………40
【表4.5】各國家股價指數報酬率PP單根檢定(水準項)……… 40
【表4.6】各國家股價指數報酬率PP單根檢定(差分項)……… 41
【表4.7】ARCH效果檢定………………………………………… 43
【表4.8】美國S&P500指數(SPX)模型估計………………………47
【表4.9】巴西聖保羅BOVESPA指數(IBOV)模型估計……………48
【表4.10】俄羅斯莫斯科ASP綜合指數(ASPGEN)模型估計…… 49
【表4.11】印度孟買SENSEX30指數(SENSEX)模型估計…………50
【表4.12】中國上海證交所綜合指數(SHCOMP)模型估計………51


圖  次
【圖3.1】SGT家族的族譜…………………………………………20
【圖4.1】美國之S&P500指數(SPX)走勢圖………………………34
【圖4.2】巴西聖保羅BOVESPA指數(IBOV)走勢圖………………34
【圖4.3】俄羅斯莫斯科ASP綜合指數(ASPGEN)走勢圖…………34
【圖4.4】印度孟買SENSEX30指數(SENSEX)走勢圖…………… 35
【圖4.5】中國上海證交所綜合指數(SHCOMP)走勢圖………… 35
【圖4.6】美國之S&P500指數(SPX)報酬走勢圖…………………41
【圖4.7】巴西聖保羅BOVESPA指數(IBOV)報酬走勢圖…………41
【圖4.8】俄羅斯莫斯科ASP綜合指數(ASPGEN)報酬走勢圖……42
【圖4.9】印度孟買SENSEX30指數(SENSEX)報酬走勢圖……… 42
【圖4.10】中國上海證交所綜合指數(SHCOMP)報酬走勢圖……42

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