Periodic Stochastic Processes

周期性随机过程

• 批准号: 0905570
• 负责人: Robert Lund
• 金额: $ 10万
• 依托单位: Clemson University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-09-01 至 2012-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0905570&HistoricalAwards=false
• 关键词: Periodic; Stochastic; Processes

The investigator will study several stochastic process problems insettings where the observations have a periodic structure. These problemsinclude 1) assessing whether or not two periodically stationary timeseries have the same dynamics, 2) the development of models for countseries in a periodic environment, and 3) assessing trends in periodicstorage processes. To do this, the investigator will investigate periodicversions of some classical Markov chain, renewal process, and time seriesmodels. Parameter estimation procedures for the developed models,including issues of parsimony, will be studied.Most processes observed in everyday life --- tides, temperatures, gasolineprices --- have a seasonal (periodic) component. This research willdevelop rigorous statistical procedures to analyze several types ofperiodic data. The applications are aimed at answering several climatechange questions including 1) are Atlantic Basin hurricane countsincreasing (periodic series of counts)?, 2) are daily snow depth series inthe United States showing change (periodic storage processes)?, and 3) canthe climate record from two neighboring towns be declared the same or arethe two localities different in some aspect (equivalence of periodicallystationary time series dynamics)?

调查者将在观测具有周期结构的环境中研究几个随机过程问题。这些问题包括1)评估两个周期平稳的时间序列是否具有相同的动力学；2)周期环境中计数序列模型的发展；3)评估周期存储过程的趋势。为此，研究人员将研究一些经典马尔可夫链、更新过程和时间序列模型的周期性版本。将研究开发的模型的参数估计程序，包括节俭问题。日常生活中观察到的大多数过程-潮汐、温度、汽油价格-都有季节性(周期性)成分。这项研究将制定严格的统计程序来分析几种类型的周期数据。这些应用程序旨在回答几个气候变化问题，包括1)大西洋盆地飓风数量是否增加(周期性计数序列)？2)美国每天的积雪深度序列是否表现出变化(周期性储存过程)？以及3)来自两个相邻城镇的气候记录是否可以被宣布为相同或在某些方面不同(周期性时间序列动力学的等价性)？