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而在计量经济学和统计学中受到越来越多的关注。对于多变量非线性时间序列，文献中很少有关于分位数回归的坚实的数学理论，尽管已有大量的工作使用最大似然估计或最小二乘估计。在本研究项目中，研究人员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。提出了几种多元泛函系数模型及相关估计方法。从理论的角度，研究人员和他的同事们基于全局/局部空间分位数回归，研究了所提出模型的估计量的渐近性质、变量选择以及参数和非参数假设检验。新的建模方法为多变量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一些现有模型和技术无法解决的问题。文中还讨论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个月期、6个月期和12个月期国库券的收益率高度相关，表现出协动性。对于这样的多变量时间序列数据，应该使用多变量模型。虽然可以为每个时间序列使用单变量模型，但它们不能捕捉不同时间序列之间的关系，因此可能效率不高。鉴于经济数据中广泛存在的非线性特征，发展多元非线性建模技术具有重要意义。研究人员提出了灵活的多变量非线性模型，并引入了前沿技术来改进模型，以实现估计的稳健性和效率。这一点非常重要，因为它放松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现实的结果。提出的变量选择方法很重要，因为经济数据往往包含许多变量。对于感兴趣的问题，应该选择哪些变量？变量选择的决定往往是武断的。这项研究将提供优秀的方法来识别这些相关变量，并使调查人员能够做出可靠的决定。拟议的假设检验方法也很重要，因为它们允许人们改进模型。在对模型进行拟合后，发现了变量之间的关系。这一发现在真实情况下是真的吗？借助于所提出的假设检验方法，可以高概率地正确回答问题，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.