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.

**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