Module Information

Module Identifier
Module Title
Academic Year
Semester 1
Mutually Exclusive
Other Staff

Course Delivery

Delivery Type Delivery length / details
Lecture 18 x 1-hour
Seminars / Tutorials 4 x 1 hour.
Practical 10 x 2 hour.
Workload Breakdown (Every 10 credits carries a notional student workload of 100 hours.) Lectures and tutorials 22 hours. Worksheets (4x5 hours) 20 hours. Practical work 20 hours. Project submission 30 hours. Private study 106 hours. Formal examination 2 hours.


Assessment Type Assessment length / details Proportion
Semester Assessment 2 Hours   conventional examination  75%
Semester Assessment 2 Hours   pratical project involving analyzing a given series fully  25%

Learning Outcomes

On completion of this module, students should be able to.
1. understand the ideas of autocorrelation;

2. calculate autocovariances and autocorrelations for linear time series models;

3. identify suitable models for different data sets;

4. use models to forecast future values and set confidence limits on them.

5. understand and analyse transfer function noise models;

6. use a computer package to identify, estimate and check models relating two time series;

7. construct forecasts using transfer function/noise models;

8. recognise the need for pre-whitening in the identification of transfer functions;

9. analyse low order multivariate ARMA models;

10. recognise cointegration and understand its implications;


To introduce students to the ideas of forecasting in a mathematical context and to the area of time series modeling.
To study models for relating two or more time series, to gain practical experience of their analysis by means of a project, to introduce some concepts in non-linear time series analysis.

Brief description

Time Series Analysis has, over the past 30 years, been one of the fastest growing areas of Statistics. It is concerned with situations where data or random variables are generated sequentially through time, and this makes the variables involved dependent on one another as opposed to having independent variables as in most other Statistics problems. This module develops a class of models to cater for such dependence, and considers how they are fitted to data, as well as how they may be used to forecast future values beyond the data set.
Many of the most important uses of time series analysis concern the relationships between two or more series. The ARIMA models introduced in the module on Time Series Analysis will be extended to cater for interventions and transfer functions and to multiple ARIMA models. The final part of the course will consider the blossoming new area of non-linear analysis. Students gain experience of the methodology by undertaking a short project


Historical background; theoretical properties of time series; the ideas of stationarity; invertibility; backward shift and difference operators
Linear Time Series Models
General linear filters. Autoregressive, Moving Average and mixed models. The ARMA family. Techniques for evaluating autocorrelation and partial autocorrelation functions. Aggregation and the case for ARMA models. Non-stationarity and ARIMA models.
Model Fitting
Identification, estimation and diagnostic checking as an iterative process. Sample autocorrelations. Least squares and conditional least squares. Differencing to achieve stationarity.
Minimum mean squared error. The Fundamental Theorem of Forecasting. Forecast error variances.
Forecasting methods
Moving averages. Exponential smoothing. Holt-Winters
Extensions of the ARIMA idea
Seasonality and SARIMA models. Time reversibility and backforecasting. Case studies.
Transfer Functions and Intervention Analysis:
Regression-autoregression models; ordinary least squares estimation and the Mann-Wald theorem. Transfer functions: interventions; impulse response function; stability and gain; crosscorrelation function, prewhitening, identif-ication of transfer functions; estimation and diagnostic checking. Forecasting.
Multiple Time Series:
The multivariate ARMA model; stationarity and invertibility, marginal models, equivalent models. Cross-covariance matrices. Co-integration.
Non-Linear Time Series: an introduction

Module Skills

Skills Type Skills details
Application of Number Throughout the module.
Communication Written worksheet solutions and project report.
Improving own Learning and Performance Feedback via tutorials.
Information Technology Extensive use of a range of computer software.
Personal Development and Career planning Students exposed to an area of Statistics that has wide applicability.
Problem solving Problem solving is central to the development and fitting of time series models, and to the ultimate goal of producing accurate forecasts of future values.
Research skills Students encouraged to consult relevant literature and compare various methods.
Subject Specific Skills General modeling ability.
Team work N/A

Reading List

General Text
Wei, William W. S. (1989.) Time series analysis :univariate and multivariate methods /William W.S. Wei. Addison-Wesley Primo search
Recommended Text
Chatfield, Christopher. (c2003.) The analysis of time series :an introduction /Chris Chatfield. 6th ed. Chapman & Hall/CRC Cryer, Jonathan D. (c2008.) Time series analysis :with applications in R /Jonathan D. Cryer, Kung-Sik Chan. 2nd ed. Springer
Supplementary Text
Box, George E. P. (c2008.) Time series analysis :forecasting and control /George E.P. Box, Gwilym M. Jenkins, Gregory C. Reinsel. 4th ed. John Wiley Primo search Hamilton, James D. (c1994.) Time series analysis /James D. Hamilton. Princeton University Press Primo search Kendall, Maurice G. (1990.) Time-series /Sir Maurice Kendall and J. Keith Ord. 3rd ed E.Arnold Primo search


This module is at CQFW Level 7