Time Series Analysis

Unit code	MATH38032
Credit rating	10
Unit level	Level 3
Teaching period(s)	Semester 2
Offered by	Department of Mathematics
Available as a free choice unit?	No

Overview

This is a statistics course. It covers some basic concepts, theory and methods for the statistical analysis of univariate time series.

Pre/co-requisites

Unit title	Unit code	Requirement type	Description
Probability 2	MATH20701	Pre-Requisite	Compulsory
Statistical Methods	MATH20802	Pre-Requisite	Compulsory
Regression Analysis	MATH38141	Recommended	Helpful

Aims

This unit aims to introduce students to some basic concepts, theory and methods of time series analysis in the univariate case.

Learning outcomes

On successful completion of this course unit students will be able to: 

· apply the concepts of stationarity, white noise, autocorrelation, and partial autocorrelation;

· write down ARMA type models and their seasonal extensions, assess causality and invertibility, and derive autocorrelations and partial autocorrelations.

· apply differencing to time series data, estimate autocorrelations and partial autocorrelations and conduct significance tests;

· apply the Box-Jenkins approach to model identification, estimation and diagnostic checking, and apply the principle of parsimony in the choice of models;

· use fitted model for forecasting and produce prediction intervals, and

· apply exponential smoothing and make connection with ARIMA modelling.

Syllabus

• Time series, stationarity, autocorrelation and partial autocorrelation, white noise, linear prediction and innovation. [3]
• AR, MA and ARMA models, causality and invertibility, derivation/computation of autocorrelations and partial auto correlations. [3] 
• Estimation of autocorrelations and partial autocorrelations. Significance tests. [2]
  Seasonal models, integrated ARMA models. [2]
• The Box-Jenkins approach to model identification, estimation and diagnostic checking. The principle of parsimony. Case studies. [5]
• Forecasting from fitted models. Prediction intervals. [3]
• Exponential smoothing and connection with ARIMA modelling. [2]

Teaching and learning methods

Two lectures and one tutorial each week. In addition students should expect to spend at least six hours each week on private study for this course unit.

Assessment methods

· Take-home coursework assignment: weighting 20%.

· End of semester examination: weighting 80%

Feedback methods

Feedback tutorials will provide an opportunity for students' work to be discussed and provide feedback on their understanding.  Coursework or in-class tests (where applicable) also provide an opportunity for students to receive feedback.  Students can also get feedback on their understanding directly from the lecturer, for example during the lecturer's office hour.

Recommended reading

· Priestley, M.B. (1981). Spectral Analysis and Time Series. [Further reading]

· Brockwell P.J. and R.A. Davis (2016). Introduction to Time Series and Forecasting. [Core]       

Study hours Scheduled activity hours
Lectures	22
Tutorials	11

Independent study hours
Independent study	67

Teaching staff

Staff member	Role
Jingsong Yuan	Unit coordinator

Additional notes

These course unit details provide the framework for delivery in 20/21 and may be subject to change due to any additional Covid-19 impact.  

Please see Blackboard/course unit related emails for any further updates.