MMath Mathematics and Statistics

Year of entry: 2027

Course unit details:
Time Series Analysis and Forecasting

Course unit fact file
Unit code MATH48032
Credit rating 15
Unit level Level 4
Teaching period(s) Semester 2
Offered by Department of Mathematics
Available as a free choice unit? No

Overview

This unit will develop further techniques of time series analysis in the time and frequency domains, for the purposes of modelling, classification and forecasting. It is suitable for students who have taken an introductory time series course.

Pre/co-requisites

Unit title Unit code Requirement type Description
Probability and Statistics 2 MATH27720 Pre-Requisite Compulsory
Linear Regression Models MATH27711 Pre-Requisite Compulsory
MATH48032 Pre-Requisites: MATH27720 and MATH27711

Students are not permitted to take MATH48032 and MATH68032 for credit in an undergraduate programme and then a postgraduate programme.

Aims

The unit aims to:

Provide advanced knowledge in time series analysis and forecasting, especially in the frequency domain and for multiple time series. 

Learning outcomes

On successful completion of this course unit students will be able to: 

  • derive statistical properties of linear time series models;  
  • conduct analysis in the frequency domain and use spectral methods to test stationarity and classify time series;
  • put univariate ARMA models in state space form and apply the Kalman filter for the evaluation of the Gaussian log-likelihood;
  • derive properties of ARCH/GARCH type models and use them for volatility forecasting;
  • extend univariate concepts and models to the multivariate case;
  • make forecasts using neural networks.

Syllabus

  • Stationarity, autocovariance function, spectrum, linear filter, frequency response.  
  • ARMA models, causality/invertibility, autocorrelation and partial autocorrelation functions.  
  • ARIMA models, exponential smoothing, recursive prediction.  
  • State space models, Kalman filter and its application in maximum likelihood estimation.  
  • Forecasting using neural networks.  
  • Spectral estimation, test of stationarity and pattern recognition.  
  • ARCH and GARCH models, volatility forecasting, extended GARCH models.  
  • Multiple time series, joint stationarity, cross-covariance/correlation matrix function, canonical and structural AR models, vector ARMA models. 

Teaching and learning methods

Teaching is composed of two hours of lectures and one tutorial class per week. One week is reserved for coursework. Teaching materials will be made available online for reference and review.

Assessment methods

Method Weight
Other 30%
Written exam 70%
  • Coursework: homework assignment weighting 30%
  • End of semester examination: weighting 70%

Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Recommended reading

  • Priestley, M.B. (1981). Spectral Analysis and Time Series. Academic Press.
  • Tsay, R.S. (2013). An Introduction to Analysis of Financial Data with R. Wiley.  
  • Tsay, R.S. (2013). Multivariate Time Series Analysis: With R and Financial Applications. Wiley.

Study hours

Scheduled activity hours
Lectures 22
Tutorials 11
Independent study hours
Independent study 117

Teaching staff

Staff member Role
Jingsong Yuan Unit coordinator

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