Course No.：S070103ZY002
Course Category：Professional Course
Period/Credits：40/2
Prerequisites：Probability theory, Statistics, Stochastic Process, Time series Analysis.
Aims & Requirements：
This course targets the Ph.D students and senior graduates in Probability theory, Statistics and Mathematical Finance. Ph.D students and senior graduates from other disciplines are encouraged to choose the course as an optional one.
This course mainly involves the recent developments of time series, which cover nonlinear time series analysis, conditional heteroscedasticity and co-integration models analysis.
Upon the successful completion of this course, the participants are expected to master the application skills and recent progress in nonlinear time series analysis.
Primary Coverage：
Chapter 1 Preliminaries for nonlinear time series
The distinctions between linear time series model and nonlinear one; nonlinear autoregressive (NAR) model; autoregressive conditional heteroscedasticity mode.
Chapter 2 Markov Chains and AR model
Markov Chains; Autoregressive modeling of Markov chains; stationarity and ergodicity of AR model; higher-order moments and tail probability properties of AR model.
Chapter 3 Statistics for nonlinear AR models
Nonlinear test; parameters estimation and order estimation for NAR model; forecasting of NAR model.
Chapter 4 Statistics for conditional heteroscedastic model
ARCH model; GARCH model; Generalized GARCH model.
Chapter 5 Multidimensional time series analysis
multidimensional AR model; multidimensional GARCH model; co-integration model.
Textbook：
Hongzhi An; Min Chen: “Nonlinear Time Series Analysis”, Shanghai Technology Press, Shanghai, 1998.
References：
[1] Howell.Tong: “Nonlinear Time Series Analysis”. Oxford Science Publication , 1990.
Author：Zhihong An (Academy of Mathematics and Systems Science)
Date：September, 2008
