# STATISTICAL METHODS WITH FINANCIAL APPLICATIONS - 2023/4

Module code: MAT3012

## Module Overview

This module introduces a variety of techniques and statistical methods widely used in discrete stochastic time series analysis. This module leads to a deeper understanding of fitting models to real data, including financial data such as monthly unemployment figures or the Financial Times Stock Exchange index. (The techniques introduced work equally well for datasets from other disciplines too such as chemistry, biology, meteorology and sport.) Essential features, such as trend and seasonality will also be identified from a dataset of interest and this will help decide on appropriate model fit. The theoretical backbone is a combination of Probability and Statistics as well as a very basic working knowledge of the statistical software R. It is noted that this is a highly theoretical module, which culminates in an extensive financial case study application.

### Module provider

Mathematics

KUEH Audrey (Maths & Phys)

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

Independent Learning Hours: 98

Lecture Hours: 28

Tutorial Hours: 11

Laboratory Hours: 4

Captured Content: 9

Semester 2

## Prerequisites / Co-requisites

Probability and Statistics (MAT1033)

## Module content

Indicative content includes:

• Example datasets from finance, business and the sciences;

• Linear filters, differencing, exponential smoothing, trend and seasonality;

• Autocorrelation and partial autocorrelation functions;

• Autoregressive and moving average (ARMA) models;

• Statistical inference for ARMA models and building strategy for ARIMA models;

• Steady growth model, linear growth model and forecasting future values;

• Using the statistical software R for choosing best-fit models and forecasting.

The module will also include ONE of the following:

• Advanced Time Series material including strategy for selecting ARIMA models and Seasonal ARMA/ARIMA models (optional content);

• Introduction to Baysian Decision Analysis and expressing business problems in a mathematical framework to deduce an optimal decision (optional content).

## Assessment pattern

Assessment type Unit of assessment Weighting
Coursework Coursework 20
Examination Exam (2 hrs) 80

N/A

## Assessment Strategy

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

• Ability to give a graphical summary of a dataset as well as use their decision-making and analysis skills to identify candidate models for further inspection.

• Subject knowledge through explicit and implicit recall of key definitions and theorems as well as interpreting this theory.

• Understanding and application of subject knowledge to perform inference tests on candidate ARMA/ARIMA models to determine a viable model to use for forecasting future values.

The summative assessment for this module consists of:

• One final examination worth 80% of the module mark.

• One coursework assignment (will take 10-20 hours to complete depending on the depth of interest taken, choice of written/typed presentation of reported statistics and the ability of the student); worth 20% of module mark.

Formative assessment and feedback Students receive individual written feedback via a number of marked formative coursework assignments over an 11-week period. The lecturer also provides verbal group feedback during lectures.

## Module aims

• Introduce students to fundamental concepts of Univariate Time Series as well as provide tools to analyse and interpret analyses of data arising from such time series to determine appropriate model fit of the dataset.
• Enable students to fit datasets to Autoregressive Integrated Moving Average (ARIMA) models.
• Illustrate key concepts of modelling datasets by demonstrating theory and enable students to deduce similar theoretical models in order to model the behaviour of a dataset with the intention of forecasting future values.

## Learning outcomes

 Attributes Developed 1 Understand results and methods of univariate time series. K 2 Apply these results and methods to analyse appropriate data. KCP 3 Interpret the results from such analyses and critically evaluate viable models to recommend the best choice. KCP 4 Know the limitations of modelling time series data and apply statistical inference to eliminate unsuitable models. KC 5 Use the statistical software R to create data summaries and to deduce best-fit models for forecasting future data values. KCPT

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 Univariate Time Series, which requires understanding the development of theoretical models and applying statistical inference to eliminate unsatisfactory models.

• Ensure experience is gained (through demonstration) of the techniques typically used to model a dataset well (with the intention of forecasting future values) so that students can later apply their own decision-making to model viable datasets that they encounter.

The learning and teaching methods include:

• 3 x 1 hour lectures per week for 9 weeks and 2 x 1 lectures per week for 2 weeks, including notes plus extra examples written and worked through on the board (or projector-display) to supplement the printed Lecture Notes that are provided at the beginning of the semester. This also includes Q&A opportunities for students.

• 1 x 1 hour lab session (once every fortnight for four weeks) for hands-on learning of the statistical software R with Lab Demonstrators on standby to assist students with their questions.

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: MAT3012

## Programmes this module appears in

Programme Semester Classification Qualifying conditions
Mathematics with Statistics MMath 2 Compulsory A weighted aggregate mark of 40% is required to pass the module
Mathematics with Statistics BSc (Hons) 2 Compulsory 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
Mathematics with Music BSc (Hons) 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 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
Mathematical 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 2023/4 academic year.