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Abstract:
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This talk proposes some new but simple methods of modeling stationary time series of integer counts. Previous work has focused on thinning methods and classical time series autoregressive moving-average (ARMA) difference equations; in contrast, our methods bypass ARMA tactics by using a stationary renewal process to generate a correlated sequence of Bernoulli trials. By superpositioning independent copies of such sequences, stationary time series with binomial, Poisson, negative binomial, and many other discrete marginal distributions are easily built. The models are naturally parsimonious, can have negative autocorrelations and/or long-memory features, and can be statistically fitted via one-step-ahead linear prediction techniques for stationary time series. As an example, a count time series with binomial marginal distributions is fitted to counts of rainy days in consecutive weeks at Key West, Florida.
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