MA36610 - TIME SERIES AND FORECASTING

Module Identifier	MA36610
Module Title	TIME SERIES AND FORECASTING
Academic Year	2001/2002
Co-ordinator	Mr David Jones
Semester	Intended for use in future years
Next year offered	N/A
Next semester offered	N/A
Pre-Requisite	MA10020 , MA11110 , MA11310
Course delivery	Lecture	19 x 1 hour lectures
	Seminars / Tutorials	3 x 1 hour example classes
Assessment	Project report		25%
	Exam	2 Hours (written examination)	75%
	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.

Reading Lists

Books
** Recommended Text
C Chatfield. The Analysis of Time Series. Chapman & Hall
** Supplementary Text
G E P Box and G M Jenkins. Time Series Analysis: Forecasting and Control. Holden-Day
J D Hamilton. Time Series Analysis. Princeton University Press
M G Kendall and J K Ord. Time Series. Edward Arnold