On the Rounded Integer-Valued Autoregressive Process

Abstract

In recent years, there has been a growing interest in modelling integred-valued time series. In this article, we propose a modified and generalized version of the first order rounded integer-valued autoregressive RINAR(1) model, originally introduced by Kachour and Yao (2009). Indeed, this class can be considered as an alternative of classical models based on the thinning operators. Using a Markov chain method, conditions for stationarity and the existence of moments are investigated. Least squares estimator of the model parameters is considered and its consistence is established. Finally, we describe the price change data using a model of the new class.

Keywords:

• Integer-valued time series
• INAR models
• Least squares estimator
• Rounding operator
• R-INAR(p) model
• Skellam distribution

Mathematics Subject Classification:

• 62M10
• 62M20

Notes

Color versions of one or more of the figures in the article can be found online at www.tandfonline.com/lsta.