Unit information: Advanced Time Series in 2015/16

Unit name	Advanced Time Series
Unit code	MATHM6003
Credit points	10
Level of study	M/7
Teaching block(s)	Teaching Block 2C (weeks 13 - 18)
Unit director	Dr. Cho
Open unit status	Not open
Pre-requisites	MATH33800 Times Series Analysis and MATH20800 Statistics 2.
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Unit aims

Describe limitations of stationary linear time series models Introduce and describe ARCH and GARCH financial time series model. Introduce and describe locally stationary time series models. General Description of the Unit

This course builds on the Level 6 MATH33800 Time Series Analysis course that described classical stationary linear time series analysis. This course considers the suitability of classical models in a variety of settings. The course then divides naturally into two sections: 1. models which possess time-varying conditional variances (GARCH, ARCH) and 2. locally stationary time series. We introduce ARCH/GARCH models, examine their properties and methods for fitting and model criticism. We then introduce locally stationary models, examine their properties and explore methods for estimating key quantities. Real life data examples will be provided throughout where necessary.

Relation to Other Units

This course builds on MATH33800, Time Series Analysis.

Further information is available on the School of Mathematics website: http://www.maths.bris.ac.uk/study/undergrad/

Intended Learning Outcomes

Learning Objectives

At the end of the unit students should be able to:

• Model and fit simple ARCH/GARCH models
• Model and estimate key parameters for locally stationary processes
• Describe the key details relating to ARCH/GARCH models.
• Describe the key details relating to locally stationary models.

Transferable Skills

The students will gain experience of modelling and fitting advanced time series models to data. These skills are highly valued in a number of areas but especially financial data modelling.

Teaching Information

Lectures (with encouraged audience participation) plus problem and solution sheets. Some of the questions on the problem sheets will be to do with practical data analysis.

Assessment Information

100% Examination.

Raw scores on the examinations will be determined according to the marking scheme written on the examination paper. The marking scheme, indicating the maximum score per question, is a guide to the relative weighting of the questions. Raw scores are moderated as described in the Undergraduate Handbook.

Reading and References

• Priestley, M.B. (1983) Spectral analysis and time series, Academic Press.
• Hamilton, J.D. (1994) Time series analysis, Princeton University Press
• Nason, G.P. and von Sachs, R. (1999) Wavelets in time series analysis,Phil. *Trans. R. Soc. Lond. A., 357, 2511-2526
• Nason, G.P., von Sachs, R. and Kroisandt, G. (2000) Wavelet processes and adaptive estimation of the evolutionary wavelet spectrum. J. R. Statist. Soc. B, 62, 271-292.