## Brazilian Journal of Probability and Statistics

- Braz. J. Probab. Stat.
- Volume 32, Number 1 (2018), 147-171.

### Noise-indicator nonnegative integer-valued autoregressive time series of the first order

Vladica Stojanović, Dragan Randjelović, and Kristijan Kuk

#### Abstract

This paper presents a modification and, at the same time, a generalization of the linear first order nonnegative integer-valued autoregressive processes, well-known as INAR(1) processes. By using the so-called Noise-Indicator, a nonlinear model with the threshold regime and with more complex structure than the appropriate linear models was obtained. The new model, named NIINAR(1) process, has been investigated in terms of the most general, the power series distribution of its innovations. Basic stochastic properties of the NIINAR(1) model (e.g., correlation structure, over-dispersion conditions and distributional properties) are given. Also, besides of some standard parameters estimators, a novel estimation techniques, together with the asymptotic properties of the obtained estimates is described. At last, a Monte Carlo study of this process is also given, as well as its application in the analysis of dynamics of two empirical dataset.

#### Article information

**Source**

Braz. J. Probab. Stat., Volume 32, Number 1 (2018), 147-171.

**Dates**

Received: January 2016

Accepted: September 2016

First available in Project Euclid: 3 March 2018

**Permanent link to this document**

https://projecteuclid.org/euclid.bjps/1520046138

**Digital Object Identifier**

doi:10.1214/16-BJPS335

**Mathematical Reviews number (MathSciNet)**

MR3770867

**Zentralblatt MATH identifier**

06973952

**Keywords**

Noise-indicator power series distribution NIINAR(1) process parameters estimation

#### Citation

Stojanović, Vladica; Randjelović, Dragan; Kuk, Kristijan. Noise-indicator nonnegative integer-valued autoregressive time series of the first order. Braz. J. Probab. Stat. 32 (2018), no. 1, 147--171. doi:10.1214/16-BJPS335. https://projecteuclid.org/euclid.bjps/1520046138