## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 29, Number 1 (2015), 71-93.

### First order non-negative integer valued autoregressive processes with power series innovations

Marcelo Bourguignon and Klaus L. P. Vasconcellos

#### Abstract

In this paper, we introduce a first order non-negative integer valued autoregressive process with power series innovations based on the binomial thinning. This new model contains, as particular cases, several models such as the Poisson INAR(1) model (Al-Osh and Alzaid (*J. Time Series Anal.* **8** (1987) 261–275)), the geometric INAR(1) model (Jazi, Jones and Lai (*J. Iran. Stat. Soc. (JIRSS)* **11** (2012) 173–190)) and many others. The main properties of the model are derived, such as mean, variance and the autocorrelation function. Yule–Walker, conditional least squares and conditional maximum likelihood estimators of the model parameters are derived. An extensive Monte Carlo experiment is conducted to evaluate the performances of these estimators in finite samples. Special sub-models are studied in some detail. Applications to two real data sets are given to show the flexibility and potentiality of the new model.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 29, Number 1 (2015), 71-93.

**Dates**

First available in Project Euclid: 30 October 2014

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1414674776

**Digital Object Identifier**

doi:10.1214/13-BJPS229

**Mathematical Reviews number (MathSciNet)**

MR3299108

**Zentralblatt MATH identifier**

1329.62370

**Keywords**

Conditional maximum likelihood INAR(1) process power series distribution

#### Citation

Bourguignon, Marcelo; Vasconcellos, Klaus L. P. First order non-negative integer valued autoregressive processes with power series innovations. Braz. J. Probab. Stat. 29 (2015), no. 1, 71--93. doi:10.1214/13-BJPS229. https://projecteuclid.org/euclid.bjps/1414674776