A full ARMA model for counts with bounded support and its application to rainy-days time series

Motivated by a large dataset containing time series of weekly number of rainy days collected over two thousand locations across Europe and Russia for the period 2000–2010, we propose a new class of ARMA-like model for time series of bounded counts, which can also handle extra-binomial variation. We abbreviate this model as bvARMA, as it is based upon a novel operation referred to as binomial variation. After having discussed important stochastic properties and proposed a model-fitting approach relying on maximum likelihood estimation, we apply the bvARMA model family to the rainy-days time series. Results show that both bvAR and bvMA models are adequate and exhibit a similar performance. Furthermore, bvARMA results outperform those obtained by fitting ordinary discrete ARMA (NDARMA) models of the same order.