About the project: In Functional data analysis (FDA), the variable of interest can be naturally viewed as a smooth curve or function, rather than scalars in univariate analysis or vectors in multivariate analysis. The field has witnessed rapid development over the last two decades. While the central ideas and methods of FDA has achieved a certain mature level, its applications in various subjects is still in an accelerating speed.
Among them, finance is one of fields that are largely benefited from the widely use of tools from FDA. In finance, some of the prominent examples that can be naturally viewed as curves include: intraday price curves (Kokoszka et al, 2015), term structure of interest rates (Barsley, 2017), forward curves of commodity futures (Horváth et al, 2019), and price signatures (Oomen, 2019).
The nature of this PhD project is employing newly developed tools in FDA to produce new insights for financial study, which cannot be revealed from the conventional methods. Thus, your first and second chapters will mainly be applied work. It is likely that you may find some limitations in the current toolkit of FDA for some specific finance problems. Then, the third chapter can develop a new method in FDA, devoting to expand the applicability of FDA in finance.
References: Bardsley, P., Horváth, L., Kokoszka, P., & Young, G. (2017). Change point tests in functional factor models with application to yield curves. The Econometrics Journal, 20(1), 86-117.
Horváth, L., & Kokoszka, P. (2012). Inference for functional data with applications (Vol. 200). Springer Science & Business Media.
Horváth, L., Liu, Z., Rice, G., & Wang, S. (2019). A functional time series analysis of forward curves derived from commodity futures. International Journal of Forecasting.
Kokoszka, P., Miao, H., & Zhang, X. (2015). Functional dynamic factor model for Intraday price curves. Journal of Financial Econometrics, 13(2), 456-477.
Kokoszka, P., & Reimherr, M. (2017). Introduction to functional data analysis. CRC Press.
Oomen, R. (2019). Price signatures. Quantitative Finance, 19(5), 733-761.
Ramsay, J. O., & Silverman, B. W. (2005). Functional data analysis. Springer.
Pre-requisites: a solid background from mathematics or statistics with knowledge in finance; proficiency in using Matlab, R, and Python; a good understanding of major textbooks in FDA, including Ramsay and Silverman (2005), Horváth and Kokoszka (2012), Kokoszka and Reimherr (2017).
Funding note: Applicants should be able to self-fund. Once an offer is made, some bespoke support may be given with regards applying for external sources of funding to cover some costs.