Unit information: Advanced Time Series in 2013/14

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	Professor. Nason
Open unit status	Not open
Pre-requisites	None
Co-requisites	None
School/department	School of Mathematics
Faculty	Faculty of Science

Description including Unit Aims

Time series are measurements on variables collected over time. The focus of this course will be on the analysis and forecasting of financial time series, by which we mean, for example, stock indices, share prices or currency exchange rates, amongst others. Of great interest to market practitioners and theoretical statisticians alike is the ability to understand the structure and forecast time series of this type. To do this, usually a probabilistic model is required. This course will introduce two families of models designed to handle financial time series: stationary nonlinear models, and locally stationary linear models.

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.

Syllabus

Harmonization from stationarity assumptions. Examples of time-varying conditional variance. The ARCH model. The GARCH model. Estimation and model fitting. Cointegration. Locally stationarity. Locally stationary Fourier processes. Locally stationary wavelet processes. Evolutionary wavelet spectrum. Localized autocovariance. Spectral estimation.

Relation to Other Units

This course builds on MATH33800, Time Series Analysis.

Intended Learning Outcomes

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

The final assessment mark for the unit is calculated from a 1½-hour written examination in APRIL. The exam will have THREE questions. A candidate's best TWO answers will be used for assessment. Calculators of an approved type (non-programmable, no text facility) may be used.

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.