# Statistics

Listed on this page are current research projects being offered for the Vacation Scholarship Program.

For more information on this research group see: Statistics

## Predicting behaviour of Financial Systems based on Dynamical Network

(posted for 2017-2018)

Owing to several economic shocks such as Asian crisis in 1997, European currency in 1999, bankruptcy of WolrdCom in 2002 and global financial crisis (GFC) in 2008, there has been a strong interest in the development of accurate models for the dependency structure of default risk among financial firms.

Image source: Six Degrees - CNT 2013 at CSE ITKgp

As evidence in this concern, risk management measures need to be at hand in order to prepare for reducing the effect of extreme events. The aim of this project is to develop fundamental theories and tools for the identification of dependence (influence) relations among various parties in a financial network that will enable understanding systemic risk in our current financial systems. Thereby, by identifying the changes and differences of links and dependency structure in the complex financial networks, portfolio and financial managers can set up a strategy to avoid or reduce the impact of the extreme events (economic shocks such as financial crisis) in the financial market. In fact, it gives a dynamic vision to managers to identify and evaluate the consistent and fragile entities.

**Contact:** Laleh Tafakori, laleh.tafakori@unimelb.edu.au

## Statistical analysis of large-scale metabolomics data

(posted for 2016-2017)

This work will deal with statistical issues regarding handling unwanted variation in the presence of missing values in high-dimensional metabolomics data - a relatively new field in omics. Two student projects are available. The first project will assist with the development of a software package for the analysis of metabolomics data using R (https://www.r-project.org/). The second project will evaluate some of the recently developed statistical approaches for the analysis of metabolomics data in terms of handling unwanted variation and missing values. Both projects will engage directly with actual analyses using metabolomics datasets. The candidates will be based at the Centre of Epidemiology and Biostatistics in the Melbourne School of Population and Global Health, and involve collaborations with the Victorian Centre for Biostatistics and the Speed Lab, Walter and Eliza Hall Institute of Medical Research. Experience with the R software is a pre-requisite for both projects.

**Contact:** Alysha De Livera alyshad@unimelb.edu.au

## Forecasting of Realized Variance Measure

(posted for 2016-2017)

The increasing availability of high frequency data orders an alternative approach to estimate and forecast the latent volatility process. The Heterogeneous Autoregressive (HAR) model provides a flexible way to model and forecast realized volatility. According to the framework of Corsi (2009), partial volatility is defined as the volatility generated by a certain market component. We consider the problem of forecasting in the generalized HAR model in order to have a superior forecasts. The data in this project consists of high-frequency observations of trades on the S&P 100 index.

**Contact:** Laleh Tafakori laleh.tafakori@unimelb.edu.au

## Stochastic composite likelihood inference for multi-colour clonal cell data

(posted for 2015-2016)

In the age of big data, the increasing complexity of statistical models in a number of fields, including biomedical sciences, has motivated a growing interest in composite likelihood methods. Composite likelihood estimation enables us to make inferences/predictions from otherwise intractable data by compounding a number of likelihood objects defined on small data subsets.

The goal of this project is to study the statistical properties of a new composite likelihood algorithm. The Vacation Scholar will have role in implementing the methodology within the R computing environment (https://www.r-project.org/) and will carry out various statistical analyses on multi-colour clonal cancer cell data. This project involves a collaboration with the Department of Pathology at the University of Melbourne.

**Contact:** Davide Ferrari dferrari@unimelb.edu.au

## Non linear random coefficient autoregressive model

(posted for 2015-2016)

The need for autoregressive time series models based on non-Gaussian distributions has led to the

development of the class of non linear exponential autoregressive models which have marginal exponential distributions.

For some time series, transformation to an exponential distribution is more appropriate than the usual transformation to a Gaussian model. For example, in many positive-valued time series we have an exponential marginal series models using exponential variables.They give an illustrative example of a set of wind speed data which have a Weibull-like distribution and can easily be power transformed to an exponential distribution.

In this project, we will consider this specific kind of random coefficient autoregressive model and their statistical properties.

Furthermore, we also investigate the Maximum quasi likelihood estimation (MQE) which has many of the desirable properties of Maximum likelihood estimation (MLE), without requiring the existence of an objective function to be maximized. Therefore, the difficulties arising from the discontinuous likelihood function of the mentioned model can be avoided by using MQE.

**Contact:** Laleh Tafakori laleh.tafakori@unimelb.edu.au