A signed binomial autoregressive model for the bounded ℤ-valued time series

Bounded $ \mathbb {Z} $ Z-valued count time series, which take values in $ \{-N,\ldots,-1,0,1,\ldots,N\} $ {-N,& mldr;,-1,0,1,& mldr;,N} with $ N\in \mathbb {N}=\{1,2,\ldots \} $ N is an element of N={1,2,& mldr;}, are occasionally encountered in practical scenarios. For instance, they arise as the differenced series of count time series with a finite support $ \{0,1,\ldots,N\} $ {0,1,& mldr;,N}. To better fit the bounded $ \mathbb {Z} $ Z-valued count time series, this article introduces a new binomial autoregressive model based on the signed binomial thinning operator. The model properties are investigated and some closed-form estimators and their several robust versions for the model parameters are proposed. These estimators are convenient to implement since any numerical optimization procedure is not required. Furthermore, the robust closed-form estimators provide an ideal approach to deal with the outliers. Intensive simulations are conducted to evaluate and compare the proposed estimators under the circumstances of clean and contaminated data. An application to the air quality level data is conducted and the performance of the proposed estimators are assessed by in-sample and out-of-sample predictions.