<p>【书名】 Generalized Autoregressive Conditional&nbsp; Heteroscedastic Time Series Models<br/>【作者】Michael S. Lo&nbsp;&nbsp; <br/>【出版社】SIMON FRASER UNIVERSITY<br/>【出版日期】April 2003<br/>【文件格式】PDF&nbsp; 【页数】61<br/>【资料类别】计量经济文章</p><p>【内容简介】</p><p align="left">Autoregressive and Moving Average time series models and their combination are<br/>reviewed. Autoregressive Conditional Heteroscedastic (ARCH) and Generalized<br/>Autoregressive Conditional Heteroscedastic (GARCH) models are extensions of these<br/>models. These are de ned and compared to the class of Autoregressive Moving<br/>Average models. Maximum likelihood estimation of parameters is examined.<br/>Conditions for existence and stationarity of GARCH models are discussed and the<br/>moments of the observations and the conditional variance are derived. Characteristics<br/>of low order GARCH models are explored further through simulations with<br/>di erent initial parameter values. As examples, GARCH models with di erent orders<br/>are tted to the Standard &amp; Poor's 500 Stock Price Index.<br/>【目录】Contents<br/>Approval Page . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ii<br/>Abstract . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii<br/>Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv<br/>List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . viii<br/>List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix<br/>1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1<br/>2 Time Series Concepts and Models . . . . . . . . . . . . . . . . . . . . 3<br/>2.1 Stationarity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3<br/>2.2 Standard Time Series Models . . . . . . . . . . . . . . . . . . 5<br/>2.2.1 General Autoregressive Models . . . . . . . . . . . . 5<br/>2.2.2 General Moving Average Models . . . . . . . . . . . 8<br/>2.2.3 General Autoregressive Moving Average Models . . . 10<br/>2.3 Financial Time Series Models . . . . . . . . . . . . . . . . . . 12<br/>2.3.1 Autoregressive Conditional Heteroscedastic (ARCH)<br/>Models . . . . . . . . . . . . . . . . . . . . . . . . . 12<br/>2.3.2 Generalized Autoregressive Conditional Heteroscedastic<br/>(GARCH) Models . . . . . . . . . . . . . . . . . . 14<br/>2.3.3 The ARCH(q) and the GARCH(1; 1) Models . . . . . 14<br/>3 The GARCH(1; 1) Model . . . . . . . . . . . . . . . . . . . . . . . . . 16<br/>3.1 Existence of the GARCH(1; 1) Process . . . . . . . . . . . . . 16<br/>3.2 Moments of Xt and ht . . . . . . . . . . . . . . . . . . . . . . 18<br/>3.3 Stationarity of the GARCH(1; 1) Process . . . . . . . . . . . . 20<br/>vi<br/>3.4 Data Simulation . . . . . . . . . . . . . . . . . . . . . . . . . . 23<br/>3.4.1 The Likelihood Function and Estimation of<br/>Parameters . . . . . . . . . . . . . . . . . . . . . . . 23<br/>3.5 A typical GARCH(1; 1) Example . . . . . . . . . . . . . . . . 25<br/>3.5.1 Results from the Monte Carlo Simulations . . . . . . 25<br/>3.5.2 Identi ability of parameters . . . . . . . . . . . . . . 27<br/>3.6 Results from Further Simulations . . . . . . . . . . . . . . . . 31<br/>3.6.1 Characteristics and Behaviour of the Estimates . . . 31<br/>3.6.2 Negative estimates . . . . . . . . . . . . . . . . . . . 32<br/>4 Data Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34<br/>4.1 Data Description . . . . . . . . . . . . . . . . . . . . . . . . . 34<br/>4.2 Fitting ARCH(1) Models and Diagnostics . . . . . . . . . . . 39<br/>4.2.1 Ljung-Box Q-Statistic . . . . . . . . . . . . . . . . . 41<br/>4.3 Fitting GARCH(1; 1) Models . . . . . . . . . . . . . . . . . . 44<br/>4.4 Diagnostics for the GARCH(1; 1) Models . . . . . . . . . . . . 46<br/>4.5 Final Remarks . . . . . . . . . . . . . . . . . . . . . . . . . . 48<br/>Bibliography . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49<br/>vii</p><br/>

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