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Advanced Time Series (MATH M6003)

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Contents of this document:

Administrative Information

  1. Unit number and title: MATH M6003 Advanced Time Series
  2. Level: M/7
  3. Credit point value: 10 credit points
  4. Year: 12/13
  5. First Given in this form: 2007-08
  6. Unit Organiser: Guy Nason
  7. Lecturer: Dr Marina Knight
  8. Teaching block: 2
  9. Prerequisites: MATH33800 Times Series Analysis and MATH20800 Statistics 2.

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.

Teaching Methods

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.

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. 

Assessment Methods

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. From 2012-13 ONLY calculators carrying a 'Faculty of Science approved' sticker will be allowed in the examination room.

Award of Credit Points

Credit points will be awarded if a student:

  • either passes the unit; i.e. attains a final assessment mark of 50 or more,
  • or if the student attains a final assessment mark of 40 or more AND attends 90% or more of the lectures. 

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.

Texts

  • 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.

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.