MATHEMATICAL TIME SERIES - 2024/5

Module code: MAT3054

Module Overview

Time series are a collection of observations taken over time. This covers a great deal of situations such as stock markets, rainfall or even goals scored by a sports team. Features of the time series will lead to an appropriate choice of model. These models will be validated, and then can be used to forecast the future. Despite the modest pre-requisites of Level 4 Probability and Statistics (MAT1033), students will gain resourcefulness and resilience through learning mathematical proofs as well as gain digital capabilities through using R to conduct analyses of data sets and writing a report.

Module provider

Mathematics & Physics

KUEH Audrey (Maths & Phys)

Module cap (Maximum number of students): N/A

Independent Learning Hours: 61

Lecture Hours: 33

Tutorial Hours: 5

Laboratory Hours: 3

Guided Learning: 15

Captured Content: 33

Semester 2

None.

Module content

Indicative content includes:

• Introduction to stochastic processes and time series;

• Estimating the trend using global polynomial, local polynomial, exponentially weighted averages, and estimating seasonality;

• Stationarity, autocovariance functions, autocorrelation functions;

• Moving average (MA) models, including invertibility;

• Autoregressive (AR) models, including causality;

• Autoregressive moving average (ARMA) models, including simplification;

• Autoregressive integrated moving average (ARIMA) and seasonal autoregressive integrated moving average (SARIMA) models;

• Model selection using the sample autocorrelation function;

• Model validation using the residual autocorrelation function;

• Forecasting from a fitted model.

Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Assessed Coursework 20
Examination End-of-Semester Examination (2 hours) 80

N/A

Assessment Strategy

The assessment strategy is designed to provide students with the opportunity to demonstrate:¿

• Understanding and knowledge of the models for stochastic processes.

• Ability to apply this knowledge to unseen datasets to produce a report in the coursework and to answer questions in the examination.

Thus, the summative assessment for this module consists of:

• One coursework involving analysis of a dataset using R, with results written in the form of a report, corresponds to Learning Outcomes 1, 2, 5.

• A synoptic examination (2 hours), corresponds to Learning Outcomes 1, 2, 3, 4.

Formative assessment

There is one draft submission and one formative unassessed coursework over an 11 week period, designed to consolidate student learning.

Feedback

Individual written feedback is provided to students for the draft submission and the formative unassessed coursework. The draft feedback is timed such that feedback will assist students with the final assessed coursework submission. The feedback from the formative unassessed coursework and the assessed coursework will assist students with preparation for the synoptic examination. Students also receive verbal feedback during lectures, tutorials and computer lab sessions.

Module aims

• Introduce students to the methodology of modelling the underlying stochastic process from a single time series.
• Equip students with methods for estimating the trend and seasonality.
• Facilitate students' understanding of stochastic processes through theorems and proofs.
• Enable students to model the behaviour of a time series with the intention of forecasting future values.

Learning outcomes

 Attributes Developed 001 Students will understand the process of modelling the underlying stochastic process from the observed time series. K 002 Students will be able to use and justify methods relating to estimating the trend and seasonality of the underlying stochastic process. CKT 003 Students will be able to state, prove and apply theorems and formulae relating to the moving average (MA), autoregressive (AR), autoregressive moving average (ARMA), autoregressive integrated moving average (ARIMA) and seasonal autoregressive integrated moving average (SARIMA) models. CKT 004 Students will be able to demonstrate how to choose and validate an appropriate model from the observed time series, and then forecast future values of the time series. CKT 005 Students will be able to use the statistical software R to analyze a given time series and write a report which can be understood by a non-expert. CKPT

Attributes Developed

C - Cognitive/analytical

K - Subject knowledge

T - Transferable skills

P - Professional/Practical skills

Methods of Teaching / Learning

The learning and teaching strategy is designed to:

Give a detailed introduction to stochastic processes and time series and ensure experience in the methods used to choose and validate a model and forecast for a given dataset.

The learning and teaching methods include:

• Lectures per week for eleven¿weeks, with typeset notes to complement the lectures. The lectures provide a structured learning environment with opportunities for students to ask questions and to practice methods taught.

• Computer lab sessions in which students gain practical experience of analysing data sets using R.

• Tutorials for guided discussion of solutions to problem sheets (provided to students in advance for completion to reinforce their understanding and guide their learning).

• One opportunity to submit a draft for the assessed coursework. Students receive individual written feedback as guidance and suggestions for improvement before their final submission of the assessed coursework.

• One unassessed coursework to provide students with further opportunity to consolidate learning. Students receive individual written feedback on these as guidance on their progress and understanding.

• Lectures may be recorded or equivalent recordings of lecture material provided. These recordings are intended to give students the opportunity to review parts of lectures that they may not fully have understood and should not be seen as an alternative to attending lectures.

Indicated Lecture Hours (which may also include seminars, tutorials, workshops and other contact time) are approximate and may include in-class tests where one or more of these are an assessment on the module. In-class tests are scheduled/organised separately to taught content and will be published on to student personal timetables, where they apply to taken modules, as soon as they are finalised by central administration. This will usually be after the initial publication of the teaching timetable for the relevant semester.

Upon accessing the reading list, please search for the module using the module code: MAT3054

Other information

The School of Mathematics and Physics is committed to developing graduates with strengths in Digital Capabilities, Employability, Global and Cultural Capabilities, Resourcefulness and Resilience, and Sustainability. This module is designed to allow students to develop knowledge, skills, and capabilities in the following areas:

• Digital Capabilities: Students in MAT3054 are guided through analyzing time series data and thus gain experience with large data and modelling methodology.

• Employability: The assessed coursework in MAT3054 is a report which is readable by a non-expert. Students thus learn to digest difficult concepts learnt in class and communicate them efficiently and accurately.

• Global and Cultural Capabilities: Students enrolled in MAT3054 originate from a variety of countries and have a wide range of cultural backgrounds. Students are encouraged to work together during problem-solving teaching activities in tutorials and lectures, which naturally facilitates the sharing of different cultures.

• Resourcefulness and Resilience: MAT3054 teaches students analytical skills to tackle uncertainty. The statistical proficiency gained from taking the module sharpens their problem-solving abilities. This gives students tools to complete challenging assignments and thus builds their resourcefulness and resilience.

• Sustainability: Students enrolled in MAT3054 learn about time series which is used to make data-driven decisions in a vast variety of areas, including management of scarce resources and climate science.

Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Music BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Mathematics BSc (Hons) 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MPhys 2 Optional A weighted aggregate mark of 40% is required to pass the module
Mathematics and Physics MMath 2 Optional A weighted aggregate mark of 40% is required to pass the module
Economics and Mathematics BSc (Hons) 2 Optional A weighted aggregate mark of 40% is required to pass the module
Financial Data Science MSc 2 Optional A weighted aggregate mark of 40% is required to pass the module

Please note that the information detailed within this record is accurate at the time of publishing and may be subject to change. This record contains information for the most up to date version of the programme / module for the 2024/5 academic year.