A seasonal binomial autoregressive process with applications to monthly rainy-days counts

Count time series exhibiting seasonal patterns are frequently encountered in practical scenarios. For example, the number of hospital emergency service arrivals may show seasonal behavior (Moriña et al. 2011 Stat Med 30:3125–3136). Numerous models have been proposed for the analysis of seasonal count time series with an unbounded support, yet seasonal patterns in bounded count time series, which are sometimes suffered in environmental science such as the number of monthly rainy-days and air quality level data, have not received formal attention. The contribution of this article lies in coping with the modeling challenges associated with seasonal count time series with a bounded support, which is beneficial for enhancing the applicability of environmental science data. This is achieved by introducing a seasonal structure and seasonally varying model parameters into the first-order binomial autoregressive (BAR(1)) model (McKenzie 1985 J Am Water Resour Assoc 21:645–650). The probabilistic and statistical properties, marginal distribution and some special cases of the proposed model are studied. Estimation of model parameters is conducted using the Yule-Walker, conditional least squares and maximum likelihood methods. The asymptotic normality of the estimators is also presented. To demonstrate the utility of our model in environmental data, applications are carried out on the monthly number of rainy-days in two Russian cities.