Grant: $99,999 - National Science Foundation - Jul. 8, 2009
46% voted satisfied - 54% voted not satisfied - 13 vote(s) cast
Award Description: Quantile regression receives increasing attention in econometrics and statistics for its advantages over mean regression. For multivariate nonlinear time series, there is little solid mathematical theory on quantile regression in the literature, although much work has been contributed using the maximum likelihood or least squares estimation. In this research project the investigator develops spatial quantile regression modeling theory of multivariate nonlinear time series data with multivariate exogeneous variables. Several multivariate functional-coefficient models and associated estimation methods are proposed. From a theoretical perspective, the investigator and his colleagues study asymptotic properties of the estimators, variable selection, and parametric and nonparametric hypothesis testing for the proposed models, based on the global/local spatial quantile regression. The novel modeling approaches open a prosperous avenue of research in the multivariate nonlinear realm and are expected to stimulate others to address a number of problems which remain beyond the reach of existing models and techniques. The computational method for implementation of the proposed methodology is also considered. IN FINANCIAL markets, multiple time series are usually related. For example, the yields of three-month, six-month and twelve-month Treasury bills are highly related and exhibit co-movement. For such multivariate time series data, one should use multivariate models. Although univariate models for each time series may be employed, they are not able to capture the relationship among different time series and may not be efficient. Since nonlinear features widely exist in economic data, it is important to develop some multivariate nonlinear modeling techniques. The investigator proposes flexible multivariate nonlinear models and introduces cutting edge techniques to refine the models and to achieve robustness and efficiency of estimation. This is very important because it relaxes restrictive assumptions frequently used in statistical and economic research and hence enables us to achieve more accurate and realistic results. The proposed variable selection method is important because economic data often include many variables. Which variables should be chosen for the problems of interest? Decisions in variable selection are often arbitrary. The research will provide elegant methods to identify those relevant variables and enable investigators to make reliable decisions. The proposed hypothesis testing methods are also important because they allow one to refine the models. After fitting a model, a relationship between variables is discovered. Is this discovery true in the real situations? With the aid of the proposed hypothesis testing methods, the question can be correctly answered with high probability, and hence the rate of error in discovery can be reduced.
Project Description: The aim of this award is to develop quantile regression (QR) modeling theory of multivariate time series data with multivariate exogeneous variables by advancing several multivariate functional-coefficient models. Expected results include some new semi- and non- parametric modeling methods to handle multivariate nonlinear time series data and some asymptotic theory for the proposed estimators and test statistics, which furnish new and more robust tools to analyze multivariate nonlinear time series data. They will be presented at seminars and conferences, and ultimately published in scientific journals. This project provides mentoring, collaboration opportunity, dissertation motivation and financial support for 2 PhD students. It also provides a great opportunity for them to get involved in a high-quality and frontier research project in statistics and its interdisciplinary fields such as economics. In the initial stage, the PI studied many related literatures and established relationship between the multivariate threshold models and the multivariate functional-coefficient models proposed in the project. The spatial quantile regression (QR) estimation has been proposed to estimate the model parameters, and mathematical properties of the estimators for the multivariate threshold models are under study. In the meantime, the PI is also studying related computational issues on the implementation of the proposed methodology using the software MATLAB. Since the related mathematical results about the multivariate threshold models are essential to this project, the PI endeavors to derive them first and then targets at establishing related mathematical results about the functional-coefficient models. The first stage results will pave the way for the second stage results, but it takes time to establish the detailed theory. The project is in progress as expected.
Jobs Summary: NA (Total jobs reported: 0)
Project Status: Less Than 50% Completed
This award's data was last updated on Jul. 8, 2009. Help expand these official descriptions using the wiki below.