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Abstract:
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Forecasting for time series of count data remains an underdeveloped area although there are many potential applications. We address the more difficult problem with multiple structural breaks at unknown points. We assume a Poisson distribution with a mean that follows an underlying autoregressive process for each regime. We use a Markov Chain Monte Carlo (MCMC) procedure with sequential importance sampling (SIS). MCMC methods are flexible techniques for estimating the parameters in the underlying process, and SIS methods provide powerful tools to tackle high-dimensional problems like our model. We used this approach in analyzing the time series of the yearly number of Atlantic hurricanes over the past 157 years. Over that period, our model identified one structural breakpoint in 1995. The model yielded a forecast of 7.25 hurricanes for 2008, which is close to the actual number 8.
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