MATH48111 - 2007/2008
General Information
- Title: Time Series Analysis and Forecasting
- Unit code: MATH48111
- Credits: 15
- Prerequisites: MATH20801 Statistical Methods, MATH38001 Statistical Inference, MATH38011 Linear Statistical Models
- Co-requisite units: None
- School responsible: Mathematics
- Members of staff responsible: Dr. Jingsong Yuan
Specification
Aims
To teach linear time series analysis theory and practice, covering both theoretical properties and computational algorithms.
Brief Description of the unit
This 15-credit unit covers the basic theory and practice of linear time series analysis at a level suitable for 4th year MMATH students specialising in statistics. It will also be offered to MSc students in statistics as an option with 6 additional lectures.
Learning Outcomes
On successful completion of this module students will be able to
- prove the stationarity of a given time series;
- derive statistical properties of ARMA models and find best linear predictors, and
- identify, fit and forecast from an appropriate model.
Future topics requiring this course unit
None.
Syllabus
- Stationarity, autocovariances and spectrum. Spectral representation. Prediction and innovation. Singularity, regularity and Wold decomposition. [4 lectures]
- Linear models: AR, MA and ARMA and their interpretation as prediction models. Stationarity and invertibility conditions and checking. Their ACF, PACF and spectra. [6]
- Yule-Walker equations and the Levinson-Durbin algorithm. Estimation of the ACF and PACF. Estimation of ARMA model parameters and inferences. [5]
- ARIMA models and the Box-Jenkins approach. Recursive prediction. [4]
- State space models and the Kalman filter. [4]
- Multivariate ARMA models. [4]
Textbooks
- Priestley, M B, Spectral Analysis and Time Series Academic Press, London 1981.
- Brockwell P J and R A Davis, Time Series: Theory and Methods, Springer-Verlag, New York 1987.
- Chatfield, C, The Analysis of Time Series - An Introduction, Sixth Edition. Chapman and Hall/CRC, London 2004.
Teaching and learning methods
Up to three lectures plus a support class(computer class/examples class) each week. In addition students should expect to spend at least six hours each week on private study for this course unit.