Module manager: tbc
Email: tbc
Taught: Semester 2 (Jan to Jun) View Timetable
Year running 2026/27
None
| MATH2701 | Statistical Methods |
| MATH2703 | Time Series |
MATH5802M Time Series and Spectral Analysis
This module is not approved as an Elective
Time series are any data where a particular variable is observed repeatedly over time, such as climate data, stock prices, or population numbers. Unlike many other types of data, observations are typically correlated with each other. In time series analysis it is the dependence between measurements taken at different times which is important. Various statistical models can be used to try to describe this temporal structure. This module will concentrate on techniques for model identification, parameter estimation, diagnostic checking and forecasting within the autoregressive moving average family of models and their extensions. Methods to model data sets with periods of greater or lesser variation and multiple time series, where observations on one series can be used to predict another, will also be studied.
To develop statistical techniques for the analysis of data collected sequentially through time. Students will gain an appreciation of model fitting for time series data and how models can be used to forecast future observations.
Subject specific learning outcomes:
On successful completion of the module students will be able to:
Assess the stationarity of a time series, through visual inspection and through the calculation and use of a sample autocorrelation function;
Evaluate the autocorrelation function and partial autocorrelation function for AR, MA and ARMA models;
Use the autocorrelation and partial autocorrelation functions and other diagnostics to formulate, test and modify suitable hypotheses about time series models;
Use ARCH and GARCH models to describe time series data with time-dependent volatility;
Evaluate the cross-correlation function for multivariate time series data and use it to describe the relationship between time series.
Forecast future values of a time series;
Use statistical software for simulation and data analysis.
Analyse real time-series data and write a report giving and interpreting the results.
Skills learning outcomes:
On successful completion of the module students will be able to:
Communicate information about temporally-structured data through interpretation, written work and reasoning.
Use statistics packages to analyse time series data and conduct forecasting.
Understand important and critical concepts of time series modelling.
Use technology appropriately in your work and studies.
1. Stationarity, definition and identification.
2. Outline of Box-Jenkins approach through identification of model, removal of trend and seasonality, fitting, diagnostic checking, and forecasting.
3. Autocorrelation function, partial autocorrelation function. Cross-correlation function for multivariate time series.
4. AR, MA, ARMA, and ARIMA models, their autocorrelation functions, and partial autocorrelation functions. Transformations and differencing to achieve stationarity.
5. ARCH and GARCH models, definition, and model selection. Autocorrelation and partial autocorrelation of squared residuals.
6. Estimation and diagnostics. Identifying possible models using autocorrelation function, and partial autocorrelation function. Estimation, outline of maximum likelihood, conditional and unconditional least squares approaches. Diagnostic checking, methods and suggestions of possible model modification.
7. Forecasting. Minimum mean square error forecast and forecast error variance, confidence intervals for forecasts, updating forecasts, other forecasting procedures.
Additional topics that build on these may be covered as time allows. Further details of possible topics will be delivered closer to the time that the module runs.
| Delivery type | Number | Length hours | Student hours |
|---|---|---|---|
| Lecture | 33 | 1 | 33 |
| Practical | 1 | 2 | 2 |
| Private study hours | 115 | ||
| Total Contact hours | 35 | ||
| Total hours (100hr per 10 credits) | 150 | ||
115
Formative feedback will be provided on regular example sets or other similar learning activity.
Check the module area in Minerva for your reading list
Last updated: 30/04/2026
Errors, omissions, failed links etc should be notified to the Catalogue Team