- UCAS course code
- G104
- UCAS institution code
- M20
Master of Mathematics (MMath)
MMath Mathematics
Duration: 4 years
Year of entry: 2025
UCAS course code: G104 / Institution code: M20
- Key features:
Scholarships available
Accredited course
- Typical A-level offer: A*AA including specific subjects
- Typical contextual A-level offer: A*AB including specific subjects
- Refugee/care-experienced offer: A*BB including specific subjects
- Typical International Baccalaureate offer: 37 points overall with 7,6,6 at HL, including specific requirements
Course unit details:
Time Series Analysis and Forecasting
| Unit code | MATH48032 |
|---|---|
| Credit rating | 15 |
| Unit level | Level 4 |
| Teaching period(s) | Semester 2 |
| 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 |
|---|---|---|---|
| Time Series Analysis | MATH38032 | Pre-Requisite | Recommended |
| Probability and Statistics 2 | MATH27720 | Pre-Requisite | Compulsory |
| Linear Regression Models | MATH27711 | Pre-Requisite | Compulsory |
| Probability 2 | MATH20701 | Pre-Requisite | Compulsory |
| Statistical Methods | MATH20802 | Pre-Requisite | Compulsory |
| Regression Analysis | MATH38141 | Pre-Requisite | Compulsory |
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 | 24 |
| Tutorials | 12 |
| Independent study hours | |
|---|---|
| Independent study | 114 |
Teaching staff
| Staff member | Role |
|---|---|
| Jingsong Yuan | Unit coordinator |
Additional notes
The independent study hours will normally comprise the following. During each week of the taught part of the semester:
· You will normally have approximately 75-120 minutes of video content. Normally you would spend approximately 2.5-4 hrs per week studying this content independently
· You will normally have exercise or problem sheets, on which you might spend approximately 2-2.5hrs per week
· There may be other tasks assigned to you on Blackboard, for example short quizzes, short-answer formative exercises or directed reading
· In some weeks you may be preparing coursework or revising for mid-semester tests
Together with the timetabled classes, you should be spending approximately 9 hours per week on this course unit.
The remaining independent study time comprises revision for and taking the end-of-semester assessment.
The above times are indicative only and may vary depending on the week and the course unit. More information can be found on the course unit’s Blackboard page.