Noise-indicator nonnegative integer-valued autoregressive time series of the first order
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.
Keywords:
Noise-indicator / power series distribution / NIINAR(1) process / parameters estimationSource:
Brazilian journal of probability and statistics, 2018, 32, 1, 147-171Publisher:
- Brazilian Statistical Association, Sao Paulo
Funding / projects:
- New Information Technologies for Analytical Decision Making Based on Experiment Observation and their Application in Biological, Economic and Sociological Systems (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-44007)
- Interdisciplinary research of Serbian cultural and linguistic heritage. Creation of multimedial Internet portal “The Lexicon of Serbian Culture” (RS-MESTD-Integrated and Interdisciplinary Research (IIR or III)-47016)
DOI: 10.1214/16-BJPS335
ISSN: 0103-0752