Abstract
In this paper, the first-order non-negative integer-valued autoregressive process with Poisson-transmuted exponential innovations is introduced. Three estimation methods, namely, the conditional maximum likelihood, conditional least squares and Yule-Walker estimation methods are discussed to estimate the unknown parameters of the proposed process. Additionally, the simulation study is presented to assess the efficiencies of these estimation methods. Applications to two real-life data sets illustrate the usefulness of the proposed process.
Similar content being viewed by others
References
Andersson J, Karlis D (2014) A parametric time series model with covariates for integers in \(\mathbb {Z}\). Stat Model 14(2):135–156
Altun E (2019) A new generalization of geometric distribution with properties and applications. Commun Stat-Simul Comput:1–15
Altun E (2020) A new one-parameter discrete distribution with associated regression and integer-valued autoregressive models. Math Slovaca 70(4):979–994
Altun E, Cordeiro GM, Ristić MM (2021a) An one-parameter compounding discrete distribution. J Appl Stat:1–22
Altun E, Bhati D, Khan NM (2021b) A new approach to model the counts of earthquakes: INARPQX (1) process. SN Appl Sci 3(2):1–17
Al-Osh M, Alzaid A (1987) First-order integer-valued autoregressive (INAR (1)) process. J Time Ser Anal 8(3):261–275
Al-Osh MA, Aly E. E. A. (1992) First order autoregressive time series with negative binomial and geometric marginals. Communications in Statistics-Theory and Methods 21(9):2483–2492
Alzaid A, Al-Osh M (1988) First-order integer-valued autoregressive (INAR (1)) process: distributional and regression properties. Stat Neerland 42 (1):53–61
Bhati D, Kumawat P, Gómez-Déniz E (2017) A new count model generated from mixed Poisson transmuted exponential family with an application to health care data. Commun Stat-Theory Methods 46(22):11060–11076
Bourguignon M, Weiß CH (2017) An INAR (1) process for modeling count time series with equidispersion, underdispersion and overdispersion. Test 26(4):847–868
Borges P, Bourguignon M, Molinares FF (2017) A generalised NGINAR (1) process with inflated-parameter geometric counting series. Austral New Zealand J Stat 59:137–150
Bourguignon M, Vasconcellos KLP (2015) Improved estimation for Poisson INAR (1) models. J Stat Comput Simul 85:2425–2441
Bourguignon M, Rodrigues J, Santos-Neto M (2019) Extended Poisson INAR (1) processes with equidispersion, underdispersion and overdispersion. J Appl Stat 46:101–118
Ghitany ME, Al-Mutairi DK, Nadarajah S (2008) Zero-truncated Poisson-Lindley distribution and its application. Mathematics and Computers in Simulation 79(3):279–287
Jazi MA, Jones G, Lai CD (2012) Integer valued AR (1) with geometric innovations. J Iranian Stat Soc 11(2):173–190
Joe H (1997) Multivariate models and multivariate dependence concepts. Chapman & Hall, London
Kim H, Lee S (2017) On first-order integer-valued autoregressive process with Katz family innovations. J Stat Comput Simul 87:546–562
Lívio T, Mamode Khan N, Bourguignon M, Bakouch H (2018) An INAR (1) model with Poisson-Lindley innovations. Econ Bull 38:1505–1513
McKenzie E (1985) Some simple models for discrete variate time series 1. JAWRA J Amer Water Resour Assoc 21:645–650
McKenzie E (1986) Autoregressive moving-average processes with negative binomial and geometric marginal distrbutions. Adv Appl Probabx 18:679–705
MohammadPour M, Bakouch H, Shirozhan M (2018) Poisson-lindley INAR(1) model with applications. Brazil J Probab Stat 32:262–280
Ristić MM, Bakouch HS, Nastić AS (2009) A new geometric first-order integer-valued autoregressive (NGINAR (1)) process. J Stat Plann Inference 139:2218–2226
Schweer S, Weiß CH (2014) Compound Poisson INAR (1) processes: stochastic properties and testing for overdispersion. Comput Stat Data Anal 77:267–284
Weiß CH (2018) An introduction to discrete-valued time series. Wiley
Author information
Authors and Affiliations
Corresponding author
Additional information
Publisher’s Note
Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Rights and permissions
About this article
Cite this article
Altun, E., Khan, N.M. Modelling with the Novel INAR(1)-PTE Process. Methodol Comput Appl Probab 24, 1735–1751 (2022). https://doi.org/10.1007/s11009-021-09878-2
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11009-021-09878-2
Keywords
- Poisson-transmuted exponential distribution
- INAR(1) process
- Conditional maximum likelihood
- Binomial thinning
- Over-dispersion