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School of Mathematics

# MATH48111 - 2008/2009

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:
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## 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.

None.

### Syllabus

1. Stationarity, autocovariances and spectrum. Spectral representation. Prediction and innovation. Singularity, regularity and Wold decomposition. [4 lectures]
2. Linear models: AR, MA and ARMA and their interpretation as prediction models. Stationarity and invertibility conditions and checking. Their ACF, PACF and spectra. [6]
3. Yule-Walker equations and the Levinson-Durbin algorithm. Estimation of the ACF and PACF. Estimation of ARMA model parameters and inferences. [5]
4. ARIMA models and the Box-Jenkins approach. Recursive prediction. [4]
5. State space models and the Kalman filter. [4]
6. 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.

### Assessment

Coursework: 20%
End of semester written examination: two and a half hours 80%

## Arrangements

Online course materials are available for this unit.