| Abstract: | 本研究之目的在以實證方式探討我國加權股價指數日報酬率之機率分配屬性。Mantegna及Stanley提出股價報酬機率為時間距離差之線性函數,並藉以估計穩定分配的相關參數值。本研究則使用此一方法配適台灣加權股價指數日報酬率資料,結果卻發現所估計出的係數既不穩定也不合理。但是,我們若根據DuMouchel提議以Bergstrom與Feller的概似估計法,直接估計台灣加權股價指數日報酬率,而且修改使用穩定與指數混合分配的假設,結果所得到的參數估計值卻能部分支持穩定分配假設的可行性,估計指數.alpha.介於1.50與2之間。可是,在估計參數穩定性上則未如Mantegna與Stanley對美國股市資料所歸納出的結果。至於韋伯分配的假設,我們也發現參數估計值在穩定性上具有其優勢。在.zeta./sub 0/設為0的條件下,所估計出的參數具有相對的穩定性。根據Mittnik及Rachev,韋伯分配亦為穩定分配,所以韋伯分配估計參數的穩定性應有助於其作為其他財務研究之基礎假設。最後,我們若以估計參數的穩定性作為實證分配選擇的標準,則可以發現GARCH模型雖然具有大尾分配的特質,但是估計的參數值與觀察區間的長短沒有一定的關係。這意味GARCH模型的使用純為資料的配適而設計,因此與穩定分配的觀念不甚契合。
The purpose of this research project is to investigate the nature of the probability distribution of Taiwan`s stock index return. Mantegna and Stanley (1995) proposed that the probability of stock return at mean zero is a linear function of the sampling interval, and estimated the S&P500 return accordingly. They found that the probability distribution of S&P500 return is following a strict stable rule. We tried to use the same method with daily Taiwan stock index return, and found unreasonable parameter estimates. We then use Bergstrom and Feller`s expansion series to approximate the unknown probability density of stable Paretian distribution, as mentioned by DuMouchel (1971). We also adopted Mantegna and Stanley`s suggestion to mix the stable distribution with an exponential distribution. AS a result, we found some evidence to support the stable distribution assumption with .alpha. index between 1.50 and 2. The stability of parameter estimates, however, is not the same as indicated by the S&P500 data. We also found that the parameter estimates of Weibull distribution, when .zeta./sub 0/ is equal to 0, has superiority in terms of stability. According to Mittnik and Rachev, Weibull distribution is also a stable distribution. We, therefore, think Weibull distribution a potential candidate to be used as the basic distribution assumption for other financial models. Finally, we used the often cited GARCH model to fit the stock index return, and found parameter estimates are trend-less. Although GARCH model may create fat-tailed distribution, the trend-less and unpredictable parameter estimates do not give us a hint of the moving direction of parameters, if we increase the sampling interval of stock index return. In that sense, GARCH model seems not fitting the concept of stable rule well. |
