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Statistics Colloquium


Mathematics/Psychology : 103

Date & Time

February 28, 2014, 11:00 am12:00 pm


Dr. James Livsey
U.S. Census Bureau
Renewal Based Count Time Series
Count time series appear in almost every discipline, including economics, biology, meteorology and epidemiology. More specific examples are rare disease occurrences, animal sightings, and yearly hurricane totals. Basically, any data collected over time where observations are integer valued. The most popular technique for modeling Gaussian time series uses an autoregressive moving average (ARMA) recursion.

When observations are small integers, ARMA models (and the many ARMA variants included) tend to give poor forecasts and inferences. If observations have a natural marginal distribution, many techniques have been proposed, including generalized linear regression, discrete ARMA (DARMA) and integer ARMA (INARMA). However, no one model class has emerged as the most robust, flexible, and parsimonious.

This talk will discuss DARMA, INARMA and other count modeling techniques; outlining their strengths and weaknesses. Then a new renewal theory based approach is investigated. Discrete-time renewal processes are used to generate stationary sequences with the particular marginal count structure sought. The renewal class effortlessly produces Poisson, binomial, and geometric marginal count series (among others) with flexible autocovariance structures. Issues of periodicities, long-memory and multiple dimensions will be discussed.