Modelling of multivariate data with complex dependence structures using copulas

Factor copula modelling is a useful tool with many real-world applications. However, there are still several challenges that limit their widespread use. This research project aims to identify and solve some of these challenges.

The goals of this project are to:

1. Investigate and test statistical inference methods that are time-efficient and are able to tackle big data sets with spatial dependence.
2. Solve the theoretical and computational challenges regarding model selection and diagnostics.
3. Develop measures of extremal dependence that can be used to assess the strength of dependence in the tails of a multivariate distribution.

The details

Copulas are functions that “couple together” the marginal cumulative distribution functions (CDFs) of a random vector to form its joint CDF. When used in statistical modelling, copulas have the ability to estimate multivariate distributions of data - data with more than one outcome variable.

This makes copulas useful in fields like finance, where market returns are volatile and dependent on many factors. Copula modelling is used in a variety of areas in the real world. These include quantitative risk management, econometric modelling, environmental modelling.

Despite the usefulness of copula models, there are still several challenges that haven’t been addressed. Examples are:

• The lack of a model selection mechanism that can discriminate between both the number of factors and the competing types of dependence structures relating the latent factors to the observed variables
• The unreliableness of joint multivariate tail dependence measures. This is due to a lack of observational data for joint extreme events.

The essence of these challenges is summarised in the three goals above and form the basis of the research project.

Graduate researcher profile: Alex Verhoijsen

What did you do before you started your PhD?

Before I commenced my PhD, I obtained a Master of Science in Statistics from the University of Louvain-la-Neuve in Belgium as well as a Master of Science in Economics from Ghent University. During my time at Ghent, I took part in an exchange programme between Ghent University and the University of Paris-Est de Créteil.

What are the challenges of your research role? Completing a joint PhD has challenges.

The toughest part of my current role probably relates more to the organisational side of things. I’m currently based in Melbourne, but I have to liaise with my partner institution in France on a regular basis. Due to the difference in time zones, meetings can take place during non-conventional hours. While having no concrete deadlines is definitely a positive, it requires a lot of motivation, dedication, and organisation on my part to ensure that goals are met. This is definitely a role for a self-starter!

What is the best part of your research role?

My research project concerning factor copula modelling is something I’m incredibly passionate about, and my interest in this particular topic is the primary reason I decided to embark on my PhD journey.  The opportunity to work with my current supervisors Dr Pavel Krupskiy, Associate Professor Mark P. Holmes and Professor Ivan Kojadinovic is one of the highlights of my role. Collaborating with renowned researchers whose work I admire on a project I’m deeply passionate about is a dream come true.

Where do you wish to go after your PhD? Do you want to enter industry or continue doing more research?

I’m not sure yet. Both industry and academia are attractive options for me, so I’m progressing through my PhD with the intention of keeping both pathways open.

Supervision team

The University of Melbourne: Dr Pavel Krupskiy and Associate Professor Mark P. Holmes.
CNRS: Professor Ivan Kojadinovic