# School of Mathematics and Statistics

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2013/2014 Sem. 1

## Aims

To provide an introduction to the forecasting of time series using both

(a) 'classical' moving average and exponential smoothing techniques and

(b) the Box-Jenkins approach.

## Objectives

By the end of the course, students should be familiar with the topics in the syllabus given below. For appropriate types of time series, they should be able to use the computer package MINITAB to

(i) generate suitable forecasts by exponential smoothing and moving average methods;

(ii) identify and fit a suitable Box-Jenkins model, and use it to generate forecasts.

## Syllabus

- Introduction to methods of forecasting and time series models.

- Constant mean models: global constant mean process, simple moving averages, simple exponential smoothing.

- Trend Models: double moving averages for linear case, Holt's method, double exponential smoothing, higher order trend models.

- Seasonal models: additive and multiplicative seasonal effects, Holt-Winters method.

- ARIMA models: stationary stochastic processes, moving average (MA) processes, the general linear process, autoregressive (AR) processes: partial autocorrelation, ARMA processes, non-stationary models.

- Forecasting with Box-Jenkins models: minimum mean square error forecasts, properties, calculating and updating forecasts.

- Fitting Box-Jenkins models: estimating autocorrelation and partial autocorrelation coefficients, identification of ARIMA processes, seasonal models, estimation for ARMA models, model verification, brief comparison of smoothing and Box-Jenkins methods.

## Textbooks

The Analysis of Time Series : an introduction,6th ed. : C Chatfield, Chapman & Hall/CRC.

Introduction to Time Series Analysis and Forecasting: D C Montgomery, C L Jennings & M Kulahci, Wiley-Interscience.

Time Series Analysis: J D Cryer, Duxbury.

Time Series Analysis, Forecasting and Control, 4th ed.: G E P Box, G M Jenkins & G C Reinsel, Wiley.

## Assessment

2 Hour Examination = 100%

## Prerequisites

MT2004 and either one of MT3501, MT3503, MT3504, MT3606, or any MN3000 module

## Availability

Academic year 2012/13 in semester 2 at 11

Dr M Papathomas