MATH40001 Time Series Analysis and Forecasting

This is former 431/MA4001/MT4321

 SEMESTER: First
CONTACT: Dr Jingsong Yuan (Ferranti/C8) CREDIT RATING: 15
Aims: To teach time series analysis theory and practice, covering both time domain and frequency domain approaches.  
Intended Learning Outcomes:

On successful completion of the course students will be able to:     

  • Analyse time series both in the time domain and in the freq. domain

  • Identify and fit an appropriate model to time series data

  • Check the validity of a fitted time series model

  • Make forecasts and classifications

  • Write a project report                 

Pre-requisites: 371 (ex-UMIST), UM3711 (ex-VUM)
Dependent Course(s): None
Course Description: This course is suitable for 4th year MMATH students specialising in Statistics. It deals with the statistical analysis of time series data, covering topics such as ARIMA model identification, estimation, diagnostic checking, forecasting and spectral analysis.
Teaching Mode: 27 hours of lectures 
6 hours of tutorials
5 hours of (labs) - practical work
Private Study: 114 hours
Recommended Texts: Priestley, M. B. (1981) Spectral Analysis of Time Series. Academic Press, London.
Brockwell P. J. and R. A. Davis (1987). Time Series: Theory and Methods. Springer-Verlag, New York. 
Quinn, B. Q. and E. J. Hannan (2001) Estimation and Tracking of Frequency. Cambridge University Press. 
Assessment Methods: Coursework 20%, Test in Week 7.
Written examination: 80%
No. of Lectures Syllabus
3 Stationarity, autocovariances and spectrum. Spectral representation. Prediction. Wold decomposition.
3

Linear models: AR, MA and ARMA. Stationarity and invertibility conditions and checking. Characterisation using the ACF and the PACF. Derivation of the spectrum.
3 Estimation of the ACF and PACF: Levinson-Durbin algorithm. Estimation of ARMA model parameters and inferences. Tests on residuals.
3 ARIMA models and the Box-Jenkins approach. Trend and seasonality.
3 Recursive prediction from ARIMA models. The Kalman filter.
3 Order determination using AIC and BIC. Maximum entropy estimation and Burg’s algorithm.
4 Spectral estimation by smoothing the periodogram. Asymptotic bias, variance and normality. Choice of windows. Computational algorithms.
3 Detection of periodicities and estimation of frequencies.
2 Classification of time series data by spectral comparison.

Last revised August, 2006