Module Identifier MA46610 Module Title TIME SERIES AND FORECASTING Academic Year 2000/2001 Co-ordinator Mr D A Jones Semester Semester 1 Pre-Requisite MA10020 , MA11110 , MA11310 Course delivery Lecture 19 x 1hour lectures Seminars / Tutorials 3 x 1hour example classes Assessment Exam 2 Hours (written examination) 75% Project report 25% Resit assessment 2 Hours (practical examination) Project passed: assessment as above, project mark carried forward Project failed: 2 hour written examination 100% 100%

Aims
To introduce students to an active and important area of Statistics.

Learning outcomes
On completion of this module, a student should be able to:

• explain the ideas of autocorrelation;
• calculate autovariances and autocorrelations for linear time series models;
• fit suitable models to data;
• use models to forecast future values and set confidence limits on them.

Syllabus
1. INTRODUCTION: Historical background; averaging and smoothing; theoretical properties of time series; stationarity; invertibility; backward shift and difference operators.
2. LINEAR TIME SERIES MODELS: General linear filters. Autoregressive, Moving Average and mixed models. The ARMA family. Techniques for evaluating autocorrelation and partial autocorrelation functions. Aggragation and the case for ARMA models.
3. MODEL FITTING: Identification, estimation and diagnostic checking as an iterative process. Sample autocorrelations. Least squares and conditional least squares. Time reversibility and backforecasting. Case studies.
4. FORECASTING: Minimum mean squared error. The Fundamental Theorem of Forecasting. Forecast erroe variances.
5. EXTENSIONS: Differencing. Non-stationarity and ARIMA models. Seasonality and SARIMA models. Case studies.

General description
Time Series Analysis has, over the past 20 years, been one of the fastest growing areas of Statistics and is an area of active research at Aberystwyth. 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. Students gain experience of the methodology by undertaking a short project.