Periodic Stochastic Processes

研究者将研究几个随机过程问题，其中观测值具有周期性结构。这些问题包括1)评估两个周期性平稳时间序列是否具有相同的动力学，2)在周期性环境中开发国家模型，以及3)评估周期性存储过程的趋势。为此，研究者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。将研究已开发模型的参数估计程序，包括简约问题。在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。这项研究将开发严格的统计程序来分析几种类型的周期性数据。这些应用程序旨在回答几个气候变化问题，包括1)大西洋盆地的飓风数量是否在增加（周期性的一系列计数）？2)美国的日雪深系列是否有变化（周期性储存过程）？3)两个相邻城镇的气候记录是否可以宣布相同或在某些方面不同（周期平稳时间序列动力学的等效性）？

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)?