Statistical Methodology for Stochastic Systems with Parameters Jumps and Applications to Economics, Genetics and Engineering

参数跳跃随机系统的统计方法及其在经济学、遗传学和工程学中的应用

• 批准号: 1206321
• 负责人: Haipeng Xing
• 金额: $ 18.43万
• 依托单位: SUNY at Stony Brook
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2012
• 资助国家: 美国
• 起止时间: 2012-09-01 至 2016-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1206321&HistoricalAwards=false
• 关键词: Statistical; Methodology; Stochastic; Systems; Parameters

Statistical inference problems in complex stochastic systems with parameter jumps arise in science and engineering, including economics, finance, genetics, industrial quality control, and public health. An important ingredient in the solution to these problems is efficient estimation of time-varying parameters with unknown jumps. In the proposed research, the investigator studies some newly emerged stochastic models with unknown parameter jumps in different disciplines and develops the related inference procedure. In particular, four types of problems in different areas are studied in the proposal. The first investigates a semi-parametric change-point regression model and its inference procedure for abrupt changes of covariate effect in longitudinal studies. The second develops a credit rating transition model in the presence of unknown structural breaks and an estimation procedure for the analysis of the relationship between the structural breaks in the U.S. credit market and macroeconomic and firm-specific covariates. The third considers a class of Markov switching models with stochastic regimes and their applications in economic analysis of business cycles and recurrent copy number variation analysis in genomic studies. The fourth problem discusses surveillance rules in sequential surveillance problems and their applications in risk management. The investigator will show how these challenging problems in different areas can be unified and solved by the developed statistical models and inference procedures. Complex stochastic systems with unknown parameter jumps are often encountered in various scientific and engineering practices including economics, finance, biology, risk management and control. While systems with smoothly changing parameters have been discussed intensively in the literature, recent advances in natural and social sciences show the growing importance of stochastic systems with unknown parameter jumps. In current genomic research, DNA copy number variations are key genetic events in the development and progression of numerous diseases including cancer, HIV acquisition, and Alzheimer and Parkinson's disease, and an important step in studying these genetic events is to identify the regions of variations. In economic studies, the authorities are keen to have a more detailed and quantitative characterization of the real economic states, instead of some simple descriptions such as booming or recession that are commonly discussed in the economic literature, so that proper monetary and fiscal policies can be issued. In financial studies, the 2008-2009 financial crisis raises the immediate needs for the regulatory authorities that the credit market and banking systems should be regulated and monitored based on solid statistical and econometric models and procedures, and hence an early warning system should be established to surveillance the stability of financial and economic systems. The proposed research is one of the first attempts to explore the possibility of building quantitative and implementable early-warning systems for financial markets and economic activities, which aggregates microeconomic information among individual firms and banks and macroeconomic statistics from general economic activities.

具有参数跳跃的复杂随机系统中的统计推理问题出现在科学和工程领域，包括经济学、金融学、遗传学、工业质量控制和公共卫生。解决这些问题的一个重要因素是有效估计带有未知跳变的时变参数。在本研究中，研究者研究了不同学科中新出现的具有未知参数跳跃的随机模型，并开发了相关的推理程序。具体而言，建议研究了不同领域的四类问题。第一部分研究了纵向研究中协变量效应突变的半参数变点回归模型及其推理过程。第二部分发展了一个存在未知结构性断裂的信用评级过渡模型，以及一个用于分析美国信贷市场结构性断裂与宏观经济和企业特定协变量之间关系的估计程序。第三章考虑了一类具有随机机制的马尔可夫切换模型及其在经济周期的经济分析和基因组研究中的重复拷贝数变异分析中的应用。第四个问题讨论了序列监视问题中的监视规则及其在风险管理中的应用。研究者将展示如何通过发展的统计模型和推理程序来统一和解决不同领域的这些具有挑战性的问题。在经济、金融、生物学、风险管理和控制等科学和工程实践中，经常会遇到具有未知参数跳跃的复杂随机系统。虽然具有平稳变化参数的系统已经在文献中得到了深入的讨论，但自然科学和社会科学的最新进展表明具有未知参数跳跃的随机系统越来越重要。在当前的基因组研究中，DNA拷贝数变异是癌症、HIV获取、阿尔茨海默病和帕金森病等多种疾病发生发展的关键遗传事件，而确定变异区域是研究这些遗传事件的重要步骤。在经济研究中，当局热衷于对实体经济状态进行更详细和定量的描述，而不是像经济文献中经常讨论的那样，对经济繁荣或衰退进行一些简单的描述，以便出台适当的货币和财政政策。在金融研究中，2008-2009年的金融危机向监管当局提出了迫切的需求，即信贷市场和银行体系应该基于可靠的统计和计量模型和程序进行监管和监测，因此应该建立一个早期预警系统，以监测金融和经济体系的稳定性。拟议的研究是探索为金融市场和经济活动建立数量和可执行的早期预警系统的可能性的第一次尝试之一，该系统汇集了个别公司和银行的微观经济资料以及一般经济活动的宏观经济统计数据。