Multivariate and Time Series Analysis (Distance Learning)
| Code | School | Level | Credits | Semesters |
| MATH4077 | Mathematical Sciences | 4 | 20 | Autumn UK |
- Code
- MATH4077
- School
- Mathematical Sciences
- Level
- 4
- Credits
- 20
- Semesters
- Autumn UK
Summary
This course is concerned with modelling and analysing data with structural dependence. The course will cover two main topics: time series models for analysing data that arise sequentially in time, and multivariate data analysis in which the response is a vector of random variables rather than a single random variable.
Several commonly occurring time series models will be discussed and their properties derived. Methods for model identification for real time series data will be described. Techniques for estimating the parameters of a model, assessing its fit and forecasting future values will be developed. Students will gain experience of using a statistical package and interpreting its output.
For multivariate data analysis, key topics to be covered include:
- principal components analysis, whose purpose is to identify the main modes of variation in a multivariate dataset;
- modelling and inference for multivariate data, including multivariate estimating and testing, based on the multivariate normal distribution;
- classification of observation vectors into subpopulations using a training sample.
Target Students
Available to MSc Statistics Science (Distance Learning) students.
Classes
- One 1-hour tutorial each week for 10 weeks
- One 1-hour computing each week for 10 weeks
This module is designed for distance learning programmes where delivery of material will largely be asynchronous through course notes support by lecture videos, Moodle quizzes and exercises. The tutorial will be used to support and reinforce the asynchronous learning. The computer software learning will be through specially designed workbooks with support sessions through online computer labs.
Assessment
- 50% Project: Individual project comprising a written report to assess to apply advanced modelling techniques including using the statistical package R and to interpret and communicate statistical analysis. (20 pages)
- 50% Exam 1 (2-hour): Written exam to assess statistical knowledge and understanding including aspects of computational methods.
Assessed by end of autumn semester
Educational Aims
The purpose of this course is to deepen and broaden the students' knowledge of statistics by introducing them to statistical theory and methodology for handling data with structural dependencies. This understanding is developed using temporal dependence (time series) and multivariate responses. The course builds upon statistical inference and modelling techniques introduced in the core modules.Learning Outcomes
A student who completes this course successfully will be able:
L1 - state and prove standard results relating to time series and multivariate statistical theory;
L2 - to derive, calculate and explain properties of time domain models and methods;
L3 - derive multivariate statistical techniques such as principal component analysis, classification, clustering and multidimensional scaling, and understand and explain the properties of these techniques;
L4 - to derive appropriate point and interval estimators, and construct suitable test procedures;
L5 - to use the statistical software package R to fit models to data sets, assess their fit, make predictions, and identify models underlying data sets;
L6 - to analyse and explain statistical results in the context of time series and forecasting and multivariate statistics;
L7 - write a report based on the analysis of a multivariate or time series dataset;
L8 - research and synthesize a topic related to multivariate statistics or forecasting and time series.