CONDITIONAL LEAST SQUARES ESTIMATION OF THE PARAMETERS OF HIGHER ORDER RANDOM ENVIRONMENT INAR MODElS

Petra N. Laketa, Aleksandar S. Nastic

DOI Number
https://doi.org/10.22190/FUMI1903525L
First page
525
Last page
535

Abstract


Two different random environment INAR models of higher order, precisely RrNGINARmax(p) and RrNGINAR1(p), are presented as a new approach to modeling non-stationary nonnegative integer-valued autoregressive processes. The interpretation of these models is given in order to better understand the circumstances of their application to random environment counting processes. The estimation statistics, defined using the Conditional Least Squares (CLS) method, is introduced and the properties are tested on the replicated simulated data obtained by RrNGINAR models with different parameter values. The obtained CLS estimates are presented and discussed.


Keywords

Random environment; INAR(p); RrNGINAR; negative binomial thinning; geometric marginals; conditional least squares.

Keywords


random environment; INAR(p); RrNGINAR; negative binomial thinning; geometric marginals; conditional least squares

Full Text:

PDF

References


Al-Osh, M.A., Aly, E.E.A.A.: First order autoregressive time series with negative binomial and geometric marginals, Commun. Statist. Theory Meth.(1992) 21, 2483–2492.

Al-Osh, M.A., Alzaid, A.A.: First-order integer-valued autoregressive (INAR(1)) process, J. Time Ser. Anal. (1987) 8, 261–275.

Aly, E.E.A.A., Bouzar, N.: On Some Integer-Valued Autoregressive Moving Average Models, Journal of Multivariate Analysis (1994) 50, 132–151.

Alzaid, A. A., Al-Osh, M.A.: Some autoregressive moving average processes with generalized Poisson marginal distributions, Ann. Inst. Statist. Math. (1993) 45, 223–232.

Bakouch, H.S., Risti´ c, M.M. Zero Truncated Poisson Integer Valued AR(1) Model, Metrika (2010) 72(2), 265-280.

Latour, A.: Existence and stochastic structure of a non-negative integer-valued autoregressive process, J. Time Ser. Anal. (1998) 19, 439–455

McKenzie, E. : Some simple models for discrete variate time series, Water Resour. Bull.(1985) 21, 645–650.

McKenzie, E.: Autoregressive moving-average processes with negative binomial and geometric distributions, Adv. Appl. Prob. (1986) 18, 679–705.

Nastić, A.S., Ristić, M.M.: Some geometric mixed integer-valued autoregressive (INAR) models, Statistics and Probability Letters (2012) 82, 805-811.

Nastić, A.S., Ristić, M.M., Bakouch, H.S.: A combined geometric INAR(p) model based on negative binomial thinning, Mathematical and Computer Modelling (2012) 55, 1665–1672.

Nastić, A.S., Laketa, P.N., Ristić, M.M.: Random Environment Integer-Valued Autoregressive process, J. Time Ser. Anal.(2016) 37, 267–287.

Nastić, A.S., Laketa, P.N., Ristić, M.M.: Random environment INAR models of higher order, RevStat: Statistical Journal (2017)Volume 17, Number 1, January 2019

Ristić, M.M., Bakouch, H.S., Nastić, A.S.: A new geometric first-order integer-valued autoregressive (NGINAR(1)) process, J. Stat. Plan. Inference (2009) 139, 2218–2226.

Ristić, M.M., Bourguignon, M., Nastić, A.S.: Zero-Inflated NGINAR(1) process, J. Communications in Statistics - Theory and Methods (2018)

Tang, M., Wang, Y.: Asymptotic Behaviour of Random Coefficient INAR Model under Random Environment defined by Difference Equation, Advances in Difference Equations, 2014(1), 1–9.

Weiß, C.H.: The combined INAR(p) models for time series of counts, Statist. Probab. Lett. (2008) 72, 1817–1822.

Zheng, H., Basawa, I.V., Datta, S.: Inference for pth-order random coefficient integer-valued autoregressive processes, J. Time Ser. Anal. (2006) 27, 411–440.

Zheng, H., Basawa, I.V., Datta, S.: First-order random coefficient integer-valued autoregressive processes, J. Stat. Plann. Inf. (2007) 137, 212–229.




DOI: https://doi.org/10.22190/FUMI1903525L

Refbacks

  • There are currently no refbacks.




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