Outliers detection in INAR(1) model with negative binomial innovations

Abstract

Os processos de contagem, apesar de serem largamente usados na pr atica, continuam a ser alvo de investiga c~ao. Neste trabalho considera-se o processo de contagem autorregressivo de 1a ordem - INAR(1). O objetivo principal consiste em tratar o problema da dete c~ao de outliers aditivos em processos INAR(1), considerando uma distribui c~ao binomial negativa para o processo de inova c~oes. Aplica-se a abordagem bayesiana, atrav es da amostragem de Gibbs, para estimar a probabilidade de que uma observa c~ao seja afetada por um outlier. A metodologia proposta e ilustrada atrav es de v arios exemplos simulados e conjuntos de dados reais.

Discrete-valued, or so called Integer-valued, time series is widely used in practice; but still it can be considered as a new subject for research nowadays. In this context, the variables of the process take place on nite or countable in nite sets. In this work, we study rst-order INteger-valued AutoRegressive, INAR(1), processes. The main goal, however, is to develop the statistical expressions for detecting outliers for the model, by considering the distributions of innovations as negative binomial. The Binomial thinning operator is used in process. This work considers a Bayesian approach to the problem of modeling a negative binomial integer-valued autoregressive time series contaminated with additive outliers. Furthermore, we focus on computational part of detecting the outliers of INAR(1) process where we use R software. We show how Gibbs sampling can be used to detect outlying observations in INAR(1) processes.