Undergraduate

modules

Modules

MAS3911 : Time Series

Semesters
Semester 2 Credit Value: 10
ECTS Credits: 5.0

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.

Teaching Methods

Teaching Activities
Category Activity Number Length Student Hours Comment
Guided Independent StudyAssessment preparation and completion113:0013:00Revision for unseen exam
Guided Independent StudyAssessment preparation and completion12:002:00Unseen exam
Scheduled Learning And Teaching ActivitiesLecture31:003:00Problem classes
Scheduled Learning And Teaching ActivitiesLecture21:002:00Revision lectures
Scheduled Learning And Teaching ActivitiesLecture251:0025:00Formal lectures
Guided Independent StudyIndependent study26:0012:00Preparation for projects
Guided Independent StudyIndependent study26:0012:00Preparation for problem-solving exercises
Guided Independent StudyIndependent study23:006:00Review of projects
Guided Independent StudyIndependent study121:0021:00Studying, practising and gaining understanding of course material
Guided Independent StudyIndependent study22:004:00Review of problem-solving exercises
Total100:00
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. Tutorials are used to identify and resolve specific queries raised by students and to allow students to receive individual feedback on marked work. In addition, office hours (two per week) will provide an opportunity for more direct contact between individual students and the lecturer.

Assessment Methods

The format of resits will be determined by the Board of Examiners

Exams
Description Length Semester When Set Percentage Comment
Written Examination1202A85N/A
Other Assessment
Description Semester When Set Percentage Comment
Prob solv exercises2M5Problem solving exercises
Prob solv exercises2M101 Group project
Assessment Rationale And Relationship

A substantial formal unseen examination is appropriate for the assessment of the material in this module. The problem solving exercises are expected to consist of two assignments of equal weight: the exact nature of assessment will be explained at the start of the module. The individual and group projects will be of approximately equal weight. The exercises and the projects 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; these are thus formative as well as summative assessments.

Reading Lists

Timetable