Supervisor: Dr Matteo Iacopini
Project description: This 4-year full time PhD project will focus on the development of flexible Bayesian methods for modelling time series data. Furthermore, in the PhD program, there will be 4 taught course modules in the first year.
In the PhD project, we will work on developing novel statistical methodologies from a Bayesian perspective to analyse multidimensional count time series data. As an example, the project will investigate the determinant of cross-sectional dependence and cascade events in financial markets (no. of order flows) and online social media (no. of web posts containing certain keywords).
From the methodological perspective, the focus of the project will be on developing Bayesian methods that match the specific features of multiple discrete-valued time series data, such as state-space models with jumps, flexible prior specifications, and efficient parameter estimation. Owing to the interdisciplinarity of the topic, such methods are expected to be useful to model count time series from other areas of interest, such as epidemiology (no. of infected) and informatics (no. visitors of websites), which have similar features. The Bayesian approach will enable the design and adaptive estimation of complex models able to match the desiderata that are hard to estimate with classical methods.
Despite their abundance and relevance for policy analysis, the use of tensor data (i.e., multidimensional arrays) is very scant. Methods allowing the investigation of count-valued tensor time series, including numbers of co-jumps in realised covariances and word co-occurrence networks from social media data, are currently lacking. The primary goal of this PhD studentship is to contribute to this field.
Multivariate and multidimensional count time series data are characterised by peculiar features that make their modelling challenging, including persistence, self- and cross-excitation, isolated jumps, and short-lived avalanches, as well as series-specific trends.
Common statistical methods predominantly focus on static models for low-dimensional structures, whereas more sophisticated tools are needed for policy analysis and for efficiently forecasting complex data.
The methods developed during the PhD would be used to (i) disentangle, and structurally interpret, the drivers of multiple count time series; (ii) identify and forecast cross-sectional spillovers and amplification effects.
The Bayesian approach provides sufficiently flexible methods to model the peculiar features of the data and the computational techniques necessary to address the dimensionality issue.
The main questions concern modelling the cross-sectional and temporal dependence. It is fundamental to discover “lead-lag” dependencies, that is subsets of the cross-section where occurrence of events has a predictive information on occurrence of events in another subset. For example, the order flow in one security may be associated with the order flow in another security, but with a time lag.
Another aspect regards the modelling peculiar features such as jumps and information avalanches, for example due to imitative behaviour in social media. Coupled with series-specific dynamics, this would improve the forecasting performance and allow for early detection of potentially negative cascade events.
This class of data has a wide range of interdisciplinary applications, ranging from sociology to economics and finance, from epidemiology to informatics.
Further information: How to apply Entry requirements Fees and funding