Periodic Stochastic Processes

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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)?