Statistics Colloquium : Dr. Robert Lund
This talk overviews the modeling of stationary count time series, detailing some history and recent breakthroughs. Classical work involving the discrete and integer autoregressive moving-average model classes is first reviewed. Drawbacks with these models are illuminated and used to motivate two more modern approaches: copulas and construction from stationary sequences of zeroes and ones. What emerges are very flexible model classes that are naturally parsimonious, can have negative autocorrelations and/or long-memory features, and can be statistically fitted by likelihood, composite likelihood, and/or moment methods. Various applications are pursued, including a bivariate hurricane count model with Poisson components that are negatively correlated.