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