Discrete Dynamics in Nature and Society
Volume 2009 (2009), Article ID 743685, 9 pages
Research Article

The Volatility of the Index of Shanghai Stock Market Research Based on ARCH and Its Extended Forms

1School of Science, Beijing Jiaotong University, Beijing 100044, China
2School of Economics and Management, Beijing Jiaotong University, Beijing 100044, China

Received 19 October 2009; Accepted 28 December 2009

Academic Editor: Guang Zhang

Copyright © 2009 Hao Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The proposed ARCH and its extension model have brought a powerful tool for the study of stock market volatility as well as verify that a “high risk brings high-yield” and the “leverage effect” of stock market. This paper gives modeling analysis by using the ARCH group models; in the last ten years Shanghai's index returns, concluded that there are significant “high-yield associated with high-risk” phenomenon and the “leverage effect” in the domestic securities market. The previous studies in fitting return series of ARMA models, mostly with low accuracy have a very subjective “observation autocorrelation and partial autocorrelation function method,” and even directly use “random walk” model. That will inevitably have some impact on the accuracy of the model. While this paper adopts the Pandit-Wu formulaic modeling method, the ARMA model is built on a strong theoretical foundation.