Quantile Regression for Multivariate Time Series Models with Functional Coefficients

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。分位数回归因其优于均值回归的优势而在计量经济学和统计学中受到越来越多的关注。对于多元非线性时间序列，文献中很少有可靠的分位数回归数学理论，尽管使用极大似然或最小二乘估计已经做出了很多工作。在本研究项目中，研究者发展了具有多变量外生变量的多变量非线性时间序列数据的空间分位数回归建模理论。提出了几种多元函数系数模型及其估计方法。从理论的角度来看，研究者和他的同事研究了基于全局/局部空间分位数回归的估计量的渐近性质，变量选择以及所提出模型的参数和非参数假设检验。这些新颖的建模方法为多元非线性领域的研究开辟了一条繁荣的道路，并有望激励其他人解决现有模型和技术无法解决的许多问题。本文还考虑了实现该方法的计算方法。在金融市场中，多个时间序列通常是相关的。例如，3个月、6个月和12个月国库券的收益率是高度相关的，并表现出协同波动。对于这样的多变量时间序列数据，应该使用多变量模型。虽然可以采用每个时间序列的单变量模型，但它们无法捕获不同时间序列之间的关系，并且可能效率不高。由于经济数据中广泛存在非线性特征，发展多元非线性建模技术具有重要意义。研究者提出了灵活的多元非线性模型，并引入了先进的技术来改进模型，以实现估计的鲁棒性和效率。这是非常重要的，因为它放宽了统计和经济研究中经常使用的限制性假设，从而使我们能够获得更准确和更现实的结果。由于经济数据通常包含许多变量，因此所提出的变量选择方法很重要。对于感兴趣的问题，应该选择哪些变量？变量选择中的决定通常是任意的。这项研究将提供优雅的方法来识别这些相关的变量，并使调查人员能够做出可靠的决定。提出的假设检验方法也很重要，因为它们允许人们改进模型。拟合模型后，发现变量之间的关系。这一发现在现实情况中是否正确？在提出的假设检验方法的帮助下，问题可以以高概率正确回答，从而可以降低发现的错误率。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5)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.