China's Stock Market Return Series Heteroskedasticity And Long Memory,

In stock market, what most attract you is the fluctuate price. The drive for yield made people persist on studying the law of the price fluctuate. However, the series work so complexsity that a fairly complete system,The Efficient Market Hyposysis, to explain the law of the series was raised by Fama until 1960s. In the following 40 years,the EMH is always considered as classical theory of Financial Economics. With the develop of computer technology and more abnormal phenomenas were come to light,EMH was proved not fit reality.Starting from brief introduction of the classic financial time series theory, EMH, this paper discussed the unreasonable hypothesis. The financial time series doesn't obey the normal distribution, show heteroscedasticity and long memory. Focusing on these two characters, we use the latest data, which are Index of Shanghai Stock Exchange and Shenzhen composite index, to research the heteroscedasticity and long memory.At first, this paper use ARCH theory to test the return series' heteroscedasticity.The log-likelihood and AIC both show ARMA-GARCH model is better than ARMA model, and ARMA-EGARCH is better than ARMA-GARCH and ARMA-PARCH.Second, this paper use R/S method test the long memory of the return series. and set ARFIMA model for the return series. Obviously, the ARFIMA model is better than ARMA model base on the log-likelihood and AIC.Finally, combine the heteroscedasticity and long memory of the return memory, set ARFIMA-GARCH, ARFIMA-EGARCH ARFIMA-PARCH model. From the result, we found ARFIMA-GARCH, ARFIMA-EGARCH, ARFIMA-PARCH model are better than ARMA-GARCH and ARFIMA, that is to say, when we set models for financial time series, we should consider the two characters.