- 學位論文
資產報酬在偏態GED分配下之跳躍模型比較
A comparison of GARCH –Jump Models with Skewed Generalized Error Distribution for Asset Returns
摘要
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。
並列摘要
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.