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Unit information: Financial Time Series in 2018/19

Please note: you are viewing unit and programme information for a past academic year. Please see the current academic year for up to date information.

Unit name Financial Time Series
Unit code MATHM0025
Credit points 10
Level of study M/7
Teaching block(s) Teaching Block 2D (weeks 19 - 24)
Unit director Dr. Yu
Open unit status Not open

MATH33800 Times Series Analysis and MATH20800 Statistics 2.



School/department School of Mathematics
Faculty Faculty of Science


Unit aims

This course aims to cover

  • Theoretical and practical aspects of GARCH financial time series models and variants thereof,
  • Theoretical and practical aspects of vector autoregressive co-integration in economic and financial time series models,
  • A brief introduction on statistical methods in high-frequency financial time series

General Description of the Unit

This course builds on the Level 6 MATH33800 Time Series Analysis course which describes classical stationary linear time series analysis, moves onto non-linear and non-stationary time series with an emphasis in modelling financial time series, and is concluded with a brief introduction on statistical methods used in high-frequency trading. This course aims to provide both rigorous theoretical justifications of GARCH models and error correction models, and also systematic data analysis tools from data visualisation to model evaluation, when GARCH effects or co-integration phenomenon is presented. This course will conclude with a brief introduction of statistical methods used in high-frequency financial time series, but will not cover detailed theory proofs.

Relation to Other Units

This course builds on MATH33800, Time Series Analysis.

Additional unit information can be found at

Intended learning outcomes

Learning Objectives

At the end of the unit the student should be able to

  • Understand the theoretical conditions under which the GARCH models have strictly and weakly stationary solutions.
  • Understand the sandwich estimator used in the GARCH model estimation and a deeper understanding of the robustness in general statistical procedures.
  • Examine if a certain dataset should be modelled as GARCH models, estimate and select GARCH models to fit the data, and evaluate the fitted models through the residuals.
  • Examine if a multivariate time series data are co-integrated and model the co-integration.
  • Know of basic tools to handle high-frequency financial time series.

Transferable Skills

The ability to know when different time series models work and fit suitable models are highly valued in many areas, especially in finance.

Teaching details

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

Assessment Details

100% Examination.

1.5 hours

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

Recommended reading:

Brockwell, P.J. and Davis, R.A., Time Series: Theory and Methods. Springer, (2009)
Andersen, T.G. and Davis, R.A., Handbook of Financial Time Series, Springer, (2009)
Leung Lai, T. and Xing, H., Statistical Models and Methods for Financial Markets, Springer, (2008)