A first-order autoregressive process with One-inflated Borel distribution innovations for integer values
One-inflated distributions; INAR(1) processes; Borel distribution
As time series of integer values are based on counts, such as the autoregressive processes of integer values (INAR), they may contain an excessive number of repeated values that could harm the inferential analysis if this behavior is not known. Then it becomes necessary to understand time series inflated models for integer values. Some models have been developed to study zero-inflated data, however, this work focuses on the one-inflated model (OI) and the autoregressive process with One-inflated innovations (OI-INAR(1)). Thus, the One-inflated Borel (OIB) model and the INAR(1) process with One-inflated Borel innovations (OIB-INAR(1)) are proposed. In this work, it is shown the properties of these models as well as the methods for parameters estimation.