Course Category：Professional Basic Course
Aims & Requirements：
This course is designed for the graduate and Ph.D students in all fields of mathematics, and it can also be taken as an optional or mandatory course by the graduates in other academic disciplines, such as Automatic control, Acoustics, Electronics, Mechanics ,Atmospheric Sciences,ect.
This course primarily focuses on the linear time series analysis, including time-domain methods and frequency-domain methods. The former one will cover autocorrelation analysis, ARMA modeling and linear forecasting. The latter one will involve spectral representation of stationary linear time series, the estimation of the spectral density and the detection of hidden periodicity.
Upon the successful completion of the course, the students will be able to :
Understand the concepts of the stationary linear time series and apply the theories and methods in various contexts.
Acquire the elementary skills to model the time series data empirically.
Chapter 1 Preliminaries for linear stationary time series
The stationary process; the probability distribution of stationary time series; autocorrelation; finite parameters time series model.
Chapter 2 Time series: time-domain analysis
Estimations for the mean and autocorrelation; AR, MA and ARMA modeling;
AIC criterion for model order selecting; model selection with the sparse coefficients;
Chapter 3 Time series forecasting
Linear forecasting for AMRA model
Chapter 4 Time series: frequency –domain analysis
Spectral distribution and spectral density; the spectral representation for the stationary time series and its autocovariance function.
Chapter 5 Time series: frequency-domain analysis
Discrete Fourier transform; Periodogram; window estimation for the spectral density; the detection for the hidden periodicity.
Hongzhi An “Time series analysis” Northeast Normal University Press, shanghai, 1992.
 Shuyuan He “ The applied time series”, Peking University Press, Beijing, 2003.
 Lan Gu: “ The application of time series in economics” China Statistics Press, Beijing,1994.
Author：Zhihong An (Academy of Mathematics and Systems Science)