A new thinning-based INAR(1) process for underdispersed or overdispersed counts

다국어 초록 (Multilingual Abstract)

Underdispersed and overdispersed phenomena are often observed in practice. To deal with these phenomena, we introduce a new thinning-based integer-valued autoregressive process. Some probabilistic and statistical properties of the process are obtained.
The asymptotic normality of the estimators of the model parameters, using conditional least squares, weighted conditional least squares and modified quasi-likelihood methods, are presented. One overdispersed real-data example and one underdispersed real-data example are given to show the flexibility and superiority of the new model.

참고문헌 (Reference)

1 Barreto-Souza, W., "Zero-modified geometric INAR(1)process for modelling count time series with deflation or inflation of zeros" 36 : 839-852, 2015

2 Scotto, M. G., "Thinning-based models in the analysis of integer-valued time series : A review" 15 : 590-618, 2015

3 Weiß, C. H., "Thinning operations for modeling time series of counts-a survey" 92 : 319-341, 2008

4 Weiß, C. H., "Testing for zero inflation and overdispersion in INAR(1)models" 60 : 473-498, 2019

5 Weiß, C. H., "Serial dependence and regression of Poisson INARMA models" 138 : 2975-2990, 2008

6 Cossette, H., "Risk models based on time series for count random variables" 48 : 19-28, 2011

7 Kim, H. Y., "On first-order integer-valued autoregressive process with Katz family innovations" 87 : 546-562, 2017

8 Grunwald, G., "Non-Gaussian conditional linear AR(1)models" 42 : 479-495, 2000

9 Zhu, F., "Modeling time series of counts with COM-Poisson INGARCH models" 56 : 191-203, 2012

10 Zhu, F., "Modeling overdispersed or underdispersed count data with generalized Poisson integervalued GARCH models" 389 : 58-71, 2012

11 Wagner Barreto-Souza, "Mixed Poisson INAR(1) processes" Springer Science and Business Media LLC 60 (60): 2119-2139, 2019

12 Zhang, H., "Inference for INAR(p)processes with signed generalized power series thinning operator" 140 : 667-683, 2010

13 Zheng, H., "First-order random coefficient integer-valued autoregressive processes" 137 : 212-229, 2007

14 Cong Li, "First-order mixed integer-valued autoregressive processes with zero-inflated generalized power series innovations" 한국통계학회 44 (44): 232-246, 2015

15 Alzaid, A. A., "First-order integer-valued autoregressive(INAR(1))process" 8 : 261-275, 1987

16 Jazi, M. A., "First-order integer valued AR processes with zero inflated poisson innovations" 33 : 954-963, 2012

17 Bourguignon, M., "First order non-negative integer valued autoregressive processes with power series innovations" 29 : 71-93, 2015

18 Bourguignon, M., "Extended Poisson INAR(1)processes with equidispersion, underdispersion and overdispersion" 46 : 101-118, 2019

19 Steutel, F. W., "Discrete analogues of self-decomposability and stability" 7 : 893-899, 1979

20 Weiß, C. H., "Controlling correlated processes of Poisson counts" 23 : 741-754, 2007

21 Karlsen, H., "Consistent estimates for the Near(2) and Nlar(2) time series models" 50 : 313-320, 1988

22 Schweer, S., "Compound Poisson INAR(1)processes : Stochastic properties and testing for overdispersion" 77 : 267-284, 2014

23 Freeland, R. K., "Analysis of low count time series data by Poisson autoregression" 25 : 701-722, 2004

24 Bourguignon, M., "An INAR(1)process for modeling count time series with equidispersion, underdispersion and overdispersion" 26 : 847-868, 2017

25 Risti´c, M. M., "A new geometric first-order integer-valued autoregressive(NGINAR(1))process" 139 : 2218-2226, 2009

26 Gómez-Déniz, E., "A new discrete distribution with actuarial applications" 48 : 406-412, 2011

27 Borges, P., "A geometric time series model with inflatedparameter Bernoulli counting series" 119 : 264-272, 2016