Title of Project: Dimension Reduction and Classification Algorithms

Code:
AA2122A

Supervisor:
Dr A. Artemiou

Project description:
Data mining and dimension reduction are two topics which receive great attention in the big data era we are in. There are a number of algorithms which were proposed to discuss data mining algorithms (like Support Vector Machines) and dimension reduction algorithms (like Sufficient Dimension Reduction). Recently, the two areas were combined to create new algorithms for dimension reduction in regression using ideas from the data mining literature. This created a class of new algorithms that perform very well and are able to do linear and nonlinear dimension reduction in a unified framework.
The project objective is to create first new algorithms for data mining by combining existing algorithms. The student will review the given literature and then derive results for new methodology for classification. The performance of the new algorithm will be evaluated using real datasets. Then, the algorithms will be used to perform dimension reduction to regression problems based on existing literature. Good programming skills are essential for this project. (In 2017-2018 a student work on this project and developed a modified version of SVM)

Project offered as a Double module.

Prerequisite 2nd year modules:
Definitely MA2500: Foundations of Probability and Statistics; MA2501: Programming and Statistics is helpful but not essential.

Recommended 3rd year module for concurrent study:
MA3505: Multivariate Statistics can be helpful but not required.

Number of students who can be supervised on this project:
1

Title of project:
Analysing the distribution of GARCH innovations

Code:
KS2122A

Supervisor: 
Dr. Kirstin Strokorb

Project description:
When modelling financial time series with GARCH(1,1) processes, the distribution of the GARCH innovations plays a key role in dynamic risk managment. For instance, choosing either Student-t innovations or normal innovations as a modelling approach can lead to over- or underestimation of potential risks. The literature often suggests that Student-t innovations seem to be more appropriate in most practically relevant situations. However, it has also been noted that, even when we simulate a GARCH time series with normally distributed innovations and re-estimate the innovations using standard MLE methods, the re-estimated innovations typically resemble more a Student-t sample rather than a normal one. This indicates that standard methods are typically not robust and can lead to misspecification. Sun and Zhou (2014) develop a statistical test that is based on analysing ”implied tail indices” in order to make it easier to distinguish between Student-t and normal innovations.

Guiding questions:
The aim of this project is to understand the main reasoning of this testing procedure, to implement it using statistical software, to study its performance and robustness in simulated scenarios and finally, to analyse the innovations of some real financial time series using the Sun and Zhou (2014) procedure.

Main literature suggestion (starting point):
• P. Sun and C. Zhou (2014). Diagnosing the distribution of GARCH innovations. Journal of Empirical Finance, 29, 287-303.
• conceivably references therein as needed

Project offered as double module, single module, or both:
Single

Prerequisite Modules:
Foundations of Probability and Statistics (MA2500)
Econometrics for Financial Mathematics (MA2801)
Programming and Statistics (MA2501)

Number of students who could be supervised for this project:
1

Title of Project:
Eigenvalue Problems for (large) Matrices
Code: MM2122A
Supervisor: Professor Marco Marletta
Project description:
This project is about solving the matrix eigenvalue problem Au = λu. The
ultimate aim is to deal with the case when A is a large sparse matrix, but the
student will rst study methods which are used for full matrices. For sparse
matrices, it will involve studying numerical methods which exploit the sparsity
patter, together with possible additional properties such as being Hermitian.
Many of the algorithms to be studied are described in `Matrix Computations’
by Golub and Van Loan, and are implemented in software packages such as
LAPACK and ARPACK. The ability to programme in a suitable language such
as MATLAB or Python will be important. Special methods for PDEs will also
be studied if time permits.
Prerequisite 2nd year modules:
None
Recommended 3rd year module for concurrent study:
None
Number of students who can be supervised on this project:
1

Title of Project:
Bat Impact on Turbines and Carcass Distribution

Code:
TW2122A

Supervisor:
Dr Thomas E. Woolley

Project description: We will model the impact of a bat bodies on a turbine as a simple projectile problem. Based on the stochastic distribution of bat impacts we will derive the probability density of bat carcasses. This can then be compared to data. Modelling assumptions will be updated as necessary, including air resistance and carcass rolling.

Prerequisite 2nd year modules:
MA0232 Modelling with Differential Equations,
MA2300 Mechanics II,
MA2700 Numerical Analysis II,
MA2005 Ordinary Differential Equation.
Courses in probability will also be advantageous

Recommended 3rd year module for concurrent study:
N/A

Number of students who can be supervised on this project:
1