Founding body: EPSRC
Duration: April 2003 -- March 2006
Grant Holders: Q. Yao, P. Hall and J. Penzer
In contrast to conventional time series analysis which focuses on modelling conditional first moment properties, the proposed project devotes attention to statistical inference for conditional second moments. The direct motivation lies in the increasing need to model and explain risk and uncertainty. A key application is the analysis of financial time series, although the potential uses are much wider. We intend to conduct our research on several interlocking aspects in four specified areas: (i) data-analytical methods for estimating multivariate volatility functions, including varying-coefficient fitting, and adaptive exponential smoothing, (ii) semiparametric estimation for matrix-valued volatility functions, (iii) robust estimation for volatility functions against heavy tailed distributions, and (iv) statistical inference techniques for skewness and kurtosis based on generalised empirical likelihood. The statistical techniques involved include bootstrap, back-fitting algorithm, data tilting, empirical likelihood, exponential smoothing, local linear fitting, and robust estimation. Most of our approaches are data-analytic in nature, making full use of modern computing power and accommodating large scale data analysis. Adaptive semi-parametric methods will be employed to explore local low-dimensional structure in multivariate models. We will develop and disseminate freely available software to allow our methods to be applied by others in both research and applications.
The project will fund a Post-Doctoral research position for 3 years.