# ST906 Financial Time Series

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###### Lecturer(s): Dr Yi Yu

Important: This module is only available to final year (4) integrated Masters students, MSc in Statistics students and MSc Financial Mathematics Students.

Timetable: The timetable for this module will not appear on Tabula as it is administered by WBS who use different operating systems. The module starts in term 2 week 2 and will take place Fridays 09:00-12:00 in 0.013 in WBS.

Restrictions:

Students who are not enrolled in the MSc in Financial Mathematics may take at most two of the following modules:
• ST906 Financial Time Series.
• ST909 Continuous Time Finance for Interest Rate Models.
• ST958 Advanced Topics in Mathematical Finance.

Summary:

Most financial data is available in time series form and therefore the statistics and modelling of time series data are essential components underpinning mathematical finance. The module aims to provide the relevant statistical theory and experience in financial time series statistics. One-third of the course covers exploratory and descriptive techniques for various features, such as long term level, fluctuation, distribution, linear and non-linear dependence, short and long memory dependence, directionality and volatility. Both linear and non-linear models are equally developed. Linear autoregressive moving average and nonlinear locally non-constant variance models are covered, as applicable to volatile financial returns, interest, exchange rates and futures. Ways of fitting these models to time series data, methods of their statistical validation and their use in such financial areas as forecasting, systematic trading models, fund manager evaluation, hedging and simulation are covered. The course aims to give practical experience in the use of specialized time series software for class examples and projects. .

Aims:

The Module aims to provide the student with background and skills

(a) to be able to model and analyze financial time series data, and to extend and develop methodology as required

(b) to understand and be able to critically evaluate times series developments and research results in the finance area

Learning Outcomes:

By the end of the module the student should have:

• a good theoretical understanding of the standard techniques of time series analysis as applied in the finance area
• an ability to carry out exploratory and descriptive analysis of time series data, particularly with reference to financial applications
• mathematical ability in deriving the statistical properties of linear and nonlinear time series models
• a general appreciation of nonlinearity in time series modelling, and in particular with respect to modelling volatile financial series
• an ability to undertake modelling studies of time series involving forecasting and simulation, with appropriate software, and covering model choice, fitting and validation

Content:

Examples, exploration and description of time series data: long term and local level, fluctuation, distribution, short and long term memory dependence, directionality and volatility. Use of statistical time series software. Linear modelling of time series: meaning of linearity, autoregressive and moving average models and their statistical properties, likelihood estimation and residual analysis, forecasting and simulation. Illustrative financial applications. Nonlinear modelling of financial time series: meaning of non-linearity, various non-constant conditional variance models for volatility, their statistical properties, their use in financial time series data analysis and systematic trading models, and example applications in finance. Presentation by practitioner from the finance industry showing use of time series methodology.

Organisation:

There will be one 2-hour lecture and one 1-hour seminar or problem class per week. This module runs in Term 2.

Texts:

Franke J, Hardle W and Hafner C, (2004) Statistics of Financial Markets, Springer

Cizek P, Hardle W and Weron R, (2005) Statistics for Finance and Insurance, Springer

Tsay RS, (2005) Analysis of Financial Time Series, (Second Edition), Wiley.

T L Lai & H Xing, (2008) Statistical Models and Methods for Financial Markets

Brockwell PJ and Davis RA, (2002) Introduction to Time Series and Forecasting, (Second Edition), Springer

Assessment:

Financial Time Series is examined by a single 2 hour paper at the beginning of Term 3. There is also assessed coursework in the form of three mini-projects which is weighted at 20%.

Only the marks for projects 2 & 3 are assessed.