The Research And Application Of Long Memory Time Series

Measuring the risk of a portfolio of financial assets or securities plays an important role in the field of financial economics. In this paper, the ARFIMA model is introduced to measure risk. It can describe not only volatility clustering and heteroskedasticity but also long memory of return process and volatility process, and we introduced the definition,test method and setting model of long memory time series. Using ADF KPSS test, classical R/S analysis and modified R/S analysis, we detect long memory of return series of Shanghai and Shenzhen. The results show that both return series of Shanghai and Shenzhen have strong long memory. And the long memory of Shenzhen is stronger than Shanghai. Based on these results, we use ARFIMA model to test the long memory of Shanghai and Shenzhen return series. And estimations of parameters indicate that there is long memory in the return series. The comparisons of Information Criterium demonstrate that ARFIMA(2,d,2) is most appropriate for Shenzhen and ARFIMA(3,d,2) is most appropriate for Shanghai. We get the conclusion that there is long memory exist in the stock market of China. There are many factors make the stock market has long memory and no efficient.