Module Catalogue 2026/27

Pre Requisite Comment

N/A

Co Requisite Comment

N/A

Aims

To gain an understanding of the principles of time series analysis. To develop skills for the modelling, analysis and forecasting of time series.

Module Summary
A time series is a set of ordered data with respect to time, such as the carbon dioxide concentration at a specific location measured at noon each day or the sales of a product recorded each month. Often in statistics, data are regarded as independent draws from a population. In time series analysis we typically do not regard consecutive observations to be independent, and build models to represent this dependence. Time series exhibit features such as trends and seasonal, or periodic, behaviour. In this module we consider modelling and inference for time series and forecasting future observations.

Outline Of Syllabus

Introduction to time series, including trend effects, seasonality and moving averages. Linear Gaussian processes, stationarity, autocovariance and autocorrelation. Autoregressive (AR), moving average (MA) and mixed (ARMA) models for stationary processes. Likelihood in a simple case such as AR(1). ARIMA processes, differencing, seasonal ARIMA as models for non-stationary processes. The role of sample autocorrelation, partial autocorrelation and correlograms in model choice. Tests of autocorrelation. Inference for model parameters. Forecasting. Dynamic linear models and the Kalman filter. Filtering and smoothing. Use of R for time series analysis.

Intended Knowledge Outcomes

At the end of the module it is expected that a student will be able to:

- Outline the key statistical ideas underpinning the analysis of time series data.
- Construct and select appropriate statistical models for time series data.
- Appraise the strengths and weaknesses of different approaches to modelling and forecasting time series.

Intended Skill Outcomes

At the end of the module it is expected that a student will be able to:
- Select an appropriate model for a wide variety of real-life time series data.
- Formulate an appropriate statistical analysis of such models.
- Analyse time series data appropriately in R.

Students will develop skills across the cognitive domain (Bloom’s taxonomy, 2001 revised edition): remember, understand, apply, analyse, evaluate and create.

Teaching Rationale And Relationship

Lectures are used for the delivery of theory and explanation of methods, illustrated with examples, and for giving general feedback on marked work. Problem classes are used to help develop the students’ abilities at applying the theory to solving problems.

The teaching methods are appropriate to allow students to develop a wide range of skills. From understanding basic concepts and facts to higher-order thinking.

Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The format of the examination will enable students to reliably demonstrate their own knowledge, understanding and application of learning outcomes.

Examination problems may require a synthesis of concepts and strategies from different sections, while they may have more than one way for solution. The examination time allows the students to test different strategies, work out examples and gather evidence for deciding on an effective strategy, while carefully articulating their ideas and explicitly citing the theory they are using.

The coursework assignments allow the students to develop their problem-solving techniques, to practise the methods learnt in the module, to assess their progress and to receive feedback; the summative assessment has a secondary formative purpose as well as its primary summative purpose.


Note: the exam for MAS8613 is more challenging than the exam for MAS3923.

General Notes

N/A