BSc Computer Science and Mathematics

This course unit covers a variety of concepts and models useful for empirical analysis of time series data.

To develop an understanding of the probabilistic foundations of univariate time series analysis and the ability to select, fit and assess models, construct forecasts and evaluate their uncertainty and accuracy.

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

•    apply the concepts of stationarity, white noise, autocorrelation, and partial autocorrelation;
•    formulate autoregressive moving-average (ARMA) type models and their seasonal extensions, assess causality and invertibility, and derive autocorrelations and partial autocorrelations.
•    derive best linear predictors and innovations, and apply the Yule-Walker equations, Levinson-Durbin recursion and innovations algorithm;
•    apply differencing to time series data, estimate and interpret sample autocorrelations and partial autocorrelations, and conduct significance tests;
•    apply the Box-Jenkins approach to model identification, estimation and diagnostic checking, using conditional least squares, Gaussian maximum likelihood and information criteria;
•    construct one-step and multi-step forecasts, calculate forecast error variances and prediction intervals under suitable assumptions, and apply single, double and Holt-Winters exponential smoothing;
•    use R to analyse real time series, interpret fitted models and diagnostics, and compare forecast accuracy.
 

•    Time series and stationarity. Strict and weak stationarity; Gaussian processes and white noise; autocovariance and autocorrelation; linear filtering, transformations and decomposition.
•    Linear prediction and innovations. Best linear prediction, orthogonality and innovations; partial autocorrelation; Yule-Walker equations and Levinson-Durbin recursion.
•    AR MA and ARMA models. Stationary solutions, causality and invertibility; characteristic polynomials and the backshift operator; derivation and recursive computation of autocovariances and partial autocorrelations.
•    Estimation of dependence. Sample autocovariance, autocorrelation and partial autocorrelation functions; approximate significance tests and the Ljung-Box test.
•    Seasonality and nonstationarity. Seasonal ARMA models; trend removal, ordinary and seasonal differencing; ARIMA models and the random walk.
•    Model building and assessment. Box-Jenkins identification, estimation and diagnostic checking; conditional least squares; the innovations algorithm and exact Gaussian maximum likelihood; residual diagnostics, parsimony, Akaike information criterion (AIC) and Bayesian information criterion (BIC).
•    Exponential smoothing. Single and double exponential smoothing; additive and multiplicative Holt-Winters methods; connections with ARIMA modelling.
•    Prediction and comparison. Conditional expectation and minimum mean squared error prediction; recursive one-step and multi-step forecasting; forecast error variances and Gaussian prediction intervals; forecast accuracy comparisons and real-data case studies in R.
 

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.

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.

•    Brockwell, P. J. and Davis, R. A. (2016). Introduction to Time Series and Forecasting. Core reading.
•    Priestley, M. B. (1981). Spectral Analysis and Time Series. Further reading.
 

Tuition fees for home students commencing their studies in September 2027 will be £10,050 per annum. Tuition fees for international students will be £39,700 per annum.

For general information please see the undergraduate finance pages.

All students should normally be able to complete their programme of study without incurring additional study costs over and above the tuition fee for that programme. Any unavoidable additional compulsory costs totalling more than 1% of the annual home undergraduate fee per annum, regardless of whether the programme in question is undergraduate or postgraduate taught, will be made clear to you at the point of application. Further information can be found in the University's Policy on additional costs incurred by students on undergraduate and postgraduate taught programmes (PDF document, 91KB).

The University of Manchester is committed to attracting and supporting the very best students. We have a focus on nurturing talent and ability and we want to make sure that you have the opportunity to study here, regardless of your financial circumstances.

For information about scholarships and bursaries please visit our  undergraduate student finance pages .