Financial Time Series

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

Unit description

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.

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 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.


  • Stylised facts of financial log-return data
  • Stationary solutions of GARCH models
  • Further practical issues
  • Unit-root tests
  • Co-integrated VAR
  • Introduction of high-frequency time series 

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)

Unit code: MATHM0025
Level of study: M/7 
Credit points: 10
Teaching block (weeks): 2 (19-24)
Lecturer: Dr Yi Yu


MATH33800 Times Series Analysis and MATH20800 Statistics 2



Methods of teaching

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.

Methods of Assessment

The pass mark for this unit is 50.

The final mark is calculated as follows:

  • 100% Examination (1.5 hours)

NOTE: Calculators are NOT allowed.

For information resit arrangements, please see the re-sit page on the intranet.

Please use these links for further information on relative weighting and marking criteria.

Further exam information can be found on the Maths Intranet.

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