Graduate Seminar: James Livsey (Clemson University)

Periodic Count Time Series via Stationary Renewal Processes

Discrete renewal processes are ubiquitous in stochastic phenomenon. In this talk constructing a discrete process where renewals are more (or less) likely during specified seasons is of specific interest. For example thunderstorms in the Southern United States can take place at any time in the year, but are most likely during the summer. Hurricanes, tornadoes, and snowstorms are other meteorological count processes obeying periodic dynamics. Rare disease occurrences, accidental deaths, and animal sightings are non-meteorological examples of count phenomenon following a periodic structure. In this talk a periodic version of classical discrete-time renewal sequences is developed. Given that a renewal occurs at a given time t, the time until the next renewal is allowed to depend on the season corresponding to time t. In this manner, one can build processes where renewals behave periodically. By superimposing or mixing versions of periodic renewal processes, one can construct models for periodic sequences of counts. The advantage of this method (over many time series of counts techniques like binomial thinning) is that negative autocorrelations between counts can be achieved. The methods are used to develop an autocorrelated periodic count model, fitting a stationary count model to a weekly rainfall data set that has binomial marginal distributions.

Refreshments will be served at 3:30pm in the 3rd floor lounge of Hanes Hall