A MIXED BILINEAR INAR(1) MODEL

Predrag M. Popović

DOI Number
https://doi.org/10.22190/FUMI200420012P
First page
143
Last page
156

Abstract


The paper introduces a new autoregressive model of order one for time series
of counts. The model is comprised of a linear as well as bilinear autoregressive component. These two components are governed by random coefficients. The autoregression is achieved by using the negative binomial thinning operator. The method of moments and the conditional maximum likelihood method are discussed for the parameter estimation. The practicality of the model is presented on a real data set.

Keywords

Time series of counts, Negative binomial thinning operator, Linear model, {Nonlinear} model.

Full Text:

PDF

References


M. Al-Osh and A. A. Alzaid, First-order integer-valued autoregressive (inar (1)) process, Journal of Time Series Analysis, 8 (1987), pp. 261–275.

A. Alzaid and M. Al-Osh, First-order integer-valued autoregressive (inar (1)) process: distributional and regression properties, Statistica Neerlandica, 42 (1988), pp. 53–61.

P. Doukhan, A. Latour, and D. Oraichi, A simple integer-valued bilinear time series model, Advances in Applied Probability, 38 (2006), pp. 559–578.

P. N. Laketa and A. S. Nastic, Conditional least squares estimation of the parameters of higher order random environment inar models, Facta Universitatis, Series: Mathematics and Informatics, 34 (2019), pp. 525–535.

E. McKenzie, Autoregressive moving-average processes with negative-binomial and geometric marginal distributions, Advances in Applied Probability, 18 (1986), pp. 679–705.

A. S. Nasti´c, P. N. Laketa, and M. M. Risti´c, Random environment integer-valued autoregressive process, Journal of Time Series Analysis, 37 (2016), pp. 267–287.

A. S. Nastic, P. N. Laketa, and M. M. Ristic, Random environment inar models of higher order, REVSTAT-Statistical Journal, 17 (2019), pp. 35–65.

X. Pedeli and D. Karlis, Some properties of multivariate inar (1) processes, Computational Statistics & Data Analysis, 67 (2013), pp. 213–225.

P. Popovi´c, Random coefficient bivariate inar (1) process, Facta Universitatis, Series: Mathematics and Informatics, 30 (2015), pp. 263–280.

P. M. Popovi´c and H. S. Bakouch, A bivariate integer-valued bilinear autoregressive model with random coefficients, Statistical Papers, (2018), pp. 1–22.

P. M. Popovi´c, M. M. Risti´c, and A. S. Nasti´c, A geometric bivariate time series with different marginal parameters, Statistical Papers, 57 (2016), pp. 731–753.

X. Qi, Q. Li, and F. Zhu, Modeling time series of count with excess zeros and ones based on inar (1) model with zero-and-one inflated poisson innovations, Journal of Computational and Applied Mathematics, 346 (2019), pp. 572–590.

M. M. Risti´c, H. S. Bakouch, and A. S. Nasti´c, A new geometric first-order integer-valued autoregressive (nginar (1)) process, Journal of Statistical Planning and Inference, 139 (2009), pp. 2218–2226.

M. G. Scotto, C. H.Weiß, and S. Gouveia, Thinning-based models in the analysis of integer-valued time series: a review, Statistical Modelling, 15 (2015), pp. 590–618.

F. W. Steutel and K. van Harn, Discrete analogues of self-decomposability and stability, The Annals of Probability, (1979), pp. 893–899.

C. H. Weiß, Thinning operations for modeling time series of counts—a survey, AStA Advances in Statistical Analysis, 92 (2008), p. 319.




DOI: https://doi.org/10.22190/FUMI200420012P

Refbacks

  • There are currently no refbacks.




© University of Niš | Created on November, 2013
ISSN 0352-9665 (Print)
ISSN 2406-047X (Online)