A distribuição Borel inflacionada de uns e um processo autoregressivo de primeira ordem para valores inteiros com inovações Borel inflacionada de uns

Abstract

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 Oneinflated Borel (OIB) model and the INAR(1) process with one-inflated Borel innovations (OIB-INAR(1)) are proposed. In this work the properties, such as expectation, variance, dispersion index and probability generating function, of these models are developed, as well as the methods for estimating the parameters of the OIB model, such as the method of moments and maximum likelihood. Likewise, for the OIB-INAR(1) process, the conditional least squares and conditional maximum likelihood methods, in addition to one-step-ahead prediction methodologies are studied. Finally, an application is made adjusting the OIBINAR(1) model.