Programme/Approved Electives for 2018/19
Mathematics Dual Honours (Level 6)Mathematics Major (Level 6)
Available as a Free Standing Elective
MAT-20006 Stochastic Processes
A time series is a collection of observations made sequentially, usually in time. This kind of data arises in a large number of disciplines ranging from economics and business to astrophysics and biology. This module introduces the theory, methods and applications of analysing time series data. 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.This module covers:¿ Methods for eliminating trend and seasonality.¿ Stationary time series models.¿ Autoregressive moving average (ARMA) models.¿ Parameter estimation methods for ARMA models.The module develops the following Keele Graduate attributes:1. An open and questioning approach to ideas, demonstrating curiosity and independence of thought.2. An appreciation of the development and value of Mathematics and the links between different areas of the subject.4. The ability creatively to solve problems using a range of different approaches and techniques, and to determine which techniques are appropriate for the problem at hand.6. The ability to communicate clearly and effectively in written form.
To introduce students to the extensive area of Time Series Analysis and Forecasting as a branch of statistical methodology.
Intended Learning Outcomes
apply the ideas of autocorrelation in explicit examples; will be achieved by assessments: 1,2,3calculate autocovariances and autocorrelations for linear time series models; will be achieved by assessments: 1,2,3identify and evaluate suitable models for different data sets; will be achieved by assessments: 1,2,3use models to forecast future values and set confidence limits on them; will be achieved by assessments: 1,2,3evaluate the important features of a time plot; will be achieved by assessments: 1,2,3define a time series model with deterministic trend and seasonality and a stochastic component, and apply the methods for eliminating trend and seasonality; will be achieved by assessments: 1,2,3interpret computer output as seen in practicals and exercise sheets; will be achieved by assessments: 1,2,3apply the parameter estimation methods for ARMA models. will be achieved by assessments: 1,2,3
Lecture / lab classes : 36 hoursIndependent study : 112 hoursUnseen examination : 2 hours
1: Problem Sheets weighted 10%
Description of Module Assessment
Approximately three problem sheets set at regular intervalsContinuous assessment will consist of written coursework, problem sheets, class tests, or any combination thereof.2: Project weighted 30%
Produce a report on the analysis of a time series data setAnalyse a real life data set and provide an interpretation of specialist computer output. The word length of the report should be appropriate to the problem in question.3: Exam weighted 60%
2 hour unseen examinationThe examination paper will consist of no less than five and not more than eight questions all of which are compulsory.