Multivariate data series in economics, survival analysis, medical science, biostatistics, insurance, finance, and other fields in social sciences are typically nonlinear, non-normally distributed, and have nonlinear co-movements and interactions. However, the existing econometrics and statistics methods in multivariate time series data analysis are largely confined to multivariate normal or conditional normal framework. This interdisciplinary collaborative research project will examine the estimation, testing, and empirical applications of broad classes of copula-based semiparametric models for analyzing multivariate data series that exhibit nonlinear co-movements, asymmetric, heavy-tailed, possibly censored and/or other non-normal patterns. These classes of models will partially solve the "curse-of-dimensionality" problem by specifying the marginal distributions nonparametrically (or semiparametrically) and specifying the copula functions that capture the dependence among the multivariate variables parametrically (or semiparametrically). The research will involve novel modifications and applications of several modern statistical methods such as empirical likelihood method, sieve maximum likelihood method, bootstrap method, extreme value theory, residual-based weighted empirical process theory, etc. Research outputs will include several original papers on estimation and testing of copula-based semiparametric multivariate models for independent data and for censored data, as well as estimation and testing of semiparametric dynamic models for nonlinear and possibly heavy-tailed time series data. The project will produce new estimation and testing software that can be freely downloaded from the authors' web pages. The results from this project will make significant contributions to econometrics and statistics literature on estimation and testing of semiparametric multivariate models based on copulas, tail copulas, and Garch with heavy tails, and will be very useful in economics (such as industrial organization, income inequality, health economics), insurance, biostatistics, medical science, and other fields where nonlinear dependence is important.
This project will develop new methodologies and apply modern statistical methods to explore nonlinear dependence among multivariate series and to understand complicated dynamics of human and social interactions with empirical applications to economics, insurance, finance, statistics, and other sciences. Since practitioners in finance and insurance have been combining nonlinear time series models with copulas and/or tail copulas to heuristically model multivariate option pricing, portfolio Value-at-Risk, correlated default and credit risk, and the time-varying asymmetric nonlinear co-movements among different series, the results from this project will guide applied researchers to perform statistically reliable economic policy evaluations, financial forecasts, and risk managements. The main educational plans are to train PhD students in economics, statistics, and finance to become capable researchers in related topics, and to develop new courses for students in economics, management, statistics, and quantitative finance. This award was supported as part of the fiscal year 2006 Mathematical Sciences priority area special competition on Mathematical Social and Behavioral Sciences (MSBS).
