Founding body: EPSRC
Duration: October 2005 -- February 2009
Grant Holders: H. Tong, Q. Yao and J. Penzer
This project studies models that describe linear and nonlinear relationships over time and across several time series, that is, models that describe the dependence structure in multivariate time series data. Multivariate time series consist of simultaneous observations of several related quantity's taken over time. They arise in a variety of fields including engineering, physical sciences (such as meteorology and geophysics), finance, economics and business. For example, in an engineering setting, one may be interested in the study of the simultaneous behaviour over time of current and voltage, or of pressure, temperature, and volume, whereas in economics, we may be interested in variations of interest rates, money supply and unemployment, or in say's volume, price, and advertising expenditure for a particular commodity in a business context. A conventional approach to model multivariate time series is to use the vector autoregressive moving average (VARMA) class of models. These models are inherently overparametrised; models with different parameters may have identical property's. This leads to identifiability problems. The abundance of parameters causes difficulty's in statistical inference for VARMA models; the likelihood function is typically flat. Therefore, reducing the number of parameters is a central problem in modelling multivariate time series data. In contrast to established methods, the approaches proposed in this project take advantage of modern computing power to search for simple decomposition's that represent multiple dependence structure using a small number of latent factors, therefore he number of parameters involved is much smaller than in, for example, a general VARMA representation. There is a synergy between our approach and the so-called independent component analysis, a relatively new and active research area at the boundary between information science and statistics. We will build on ideas from this field to provide decomposition's that are tailored to serve specific practical purposes. For example, our conditionally uncorrelated component-based approach offers a simple and intuitively appealing representation for the volatility's of several financial instruments. Simple representations of multiple dependence structure come at a cost; intensive computation is required to derive the relevant key components, and the associated statistical inference demands sophisticated asymptotic theory. We adopt the following strategy throughout: (i) propose and investigate promising new theory and methodological tools always guided by practical needs, (ii) test on simulated data and if simulation is successful, (iii) test on real data. the loop is likely to be repeated for further refinement.