Application Of Arfima-arch Model Of Stock Market

This article studies daily,weekly,monthly returns ratio of Shanghai stock index and Shenzhen stock index from 1996 to 2006 with the ARFIMA-EGARCH and the ARFIMA-TARCH model,in the help of EViews,S-plus and the Matlab software and compared with the corresponding ARFIMA model.At last,we found the following results:1.During studying ARFIMA-EGARCH and ARFIMA-TARCH model,we find fractal difference parameter values d of Shanghai and Shenzhen stock market are the same.Fractal difference parameter values d of daily,weekly,monthly returns ratio of Shanghai stock market and Shenzhen stock market are 0.02785(0.07397),0.035(0.07746)and 0.08835 (0.14617).In the corresponding ARFIMA model studying,we obtain fractal difference parameter values d of daily,weekly,monthly returns ratio of Shanghai stock market and Shenzhen stock market and they are 0.0268(0.08878),0.09122(0.07746)and 0.08835 (0.14617).These data certified that Shanghai and Shenzhen Stock markets have the long memory,and the volatility of the capital market have a widespread fractal features. Moreover whatever in Shanghai stock market or Shenzhen stock market,the long-term memory of returns ratio strengthens with the time interval enhance growth,that is long-term memory of daily,weekly and monthly returns ratio of Shanghai and Shenzhen stock market strengthens in turn.However,long-term memory of Shenzhen stock market is stronger than which of Shanghai stock market,that is Shenzhen Stock market's fractal features is more common.2.Not only in ARFIMA-EGARCH model,but also in ARFIMA-TARCH model,the daily returns ratio of Shanghai and Shenzhen stock market have the leverage effect,but the leverage effect of weekly and monthly returns ratio is not obvious.3.By likelihood function and AIC criterion,we can see,if data exists ARCH effect, both the ARFIMA-EGARCH and the ARFIMA-TARCH models are better than the ARFIMA model.