在现代金融行业的研究与分析中，时间序列分析的发展历史虽然只有短短30年，却占有举足轻重的地位。本文就ARCH/GARCH模型的发展历史展开论述，以ARCH/GARCH模型的发展背景入手，介绍了金融时间序列及其分析的相关背景及特征,并进一步分别介绍了针对ARCH/GARCH模型局限性而产生的T-GARCH以及E-GARCH等GARCH族模型。 而后，本文分别选取了三九医药和招商银行这两只股票，根据其股价时间序列随时间变化的不同特点，采用不同的时间序列模型在计量经济学软件Eviews中进行建模并比较最佳模型，在实证分析的过程中深入地对比理解GARCH，TGARCH以及EGARCH模型的各自特点与优势。最后，由各模型的预报结果以及模型效果的研究比对可以看出，对三九医药股价的对数收益率序列建立ARMA模型后的最优异方差模型为GARCH(1,0)模型。而后本文对招商银行的线性回归模型的残差建模中，AR(1)-GARCH(1,1)和AR(1)-EGARCH(2,1)模型都有很好的效果。

In the analysis and research of modern Finance, time series analysis secures a significant position despite its short span of 30 years of time. This paper begins with the developing history of ARCH/GARCH model, introduces related background in financial time series, describes the limitations of the GARCH model and reviews T-GARCH, E-GARCH and some other members in the families of GARCH models corresponding with the previous mentioned limitations. Then, two stock prices are picked for further empirical analysis and application. According to the characteristics of variation in stock price, different models are applied and compared in the software Eviews. In the empirical analysis, GARCH, TGARCH and EGARCH are compared and their advantages and drawbacks are discussed. In the end, based on the prediction of stock price and the significance of the model, the best model for both stocks are presented. For the error series of both stocks, GARCH(1,0) is the best suit for Sanjiu Pharmacy; AR(1)-EGARCH(2,1) and AR(1)-GARCH(1,1) both demonstrate its value in the prediction of error series from the linear model of China Merchants Bank.