A GQL estimation approach for analysing non-stationary over-dispersed BINAR(1) time series

References

• Mamode Khan N, Sunecher Y, Jowaheer V. Modelling a non-stationary BINAR(1) Poisson process. J Stat Comput Simul. 2016;86:3106–3126. doi: 10.1080/00949655.2016.1150482
   Web of Science ®Google Scholar
• Mamode Khan N, Sunecher Y, Jowaheer V. Inferential methods for an unconstrained nonstationary BINMA time series process with Poisson innovations. J Stat Theory Pract. 2016;11(1):76–106. doi: 10.1080/15598608.2016.1258600
   Web of Science ®Google Scholar
• Pedeli X, Karlis D. A bivariate INAR(1) process with application. Stat Model. 2011;11:325–349. doi: 10.1177/1471082X1001100403
   Web of Science ®Google Scholar
• Sunecher Y, Mamodekhan N, Jowaheer V. Estimating the parameters of a BINMA Poisson model for a non-stationary bivariate time series. Comm Statist Simulation Comput. 2016.
   Web of Science ®Google Scholar
• Marshall A, Olkin I. Multivariate distribution generated from mixtures of convolution and product families. In: Block, Sampson Y Sanits, editors. Topics in statistical dependence. Stanford (CA): Institute of Mathematical Statistics; 1990.
   Google Scholar
• Pedeli X, Karlis D. Bivariate INAR(1) models. Athens University of Economics; 2009. (Technical report).
   Google Scholar
• Mallick TS, Sutradhar BC. GQL versus conditional GQL inferences for non-stationary time series of counts with overdispersion. J Time Ser Anal. 2008;29(2):402–420. doi: 10.1111/j.1467-9892.2007.00570.x
   Web of Science ®Google Scholar
• Aly E-EAA, Bouzar N. Stationary solutions for integer-valued autoregressive processes. Int J Math Math Sci. 2005;2005(1):1–18. doi: 10.1155/IJMMS.2005.1
   Google Scholar
• Bourguignon M, Vasconcellos KLP. Improved estimation for Poisson INAR(1) models. J Stat Comput Simul. 2015;85(12):2425–2441. doi: 10.1080/00949655.2014.930862
   Web of Science ®Google Scholar
• McKenzie E. Some ARMA models for dependent sequences of Poisson counts. Adv Appl Probab. 1988;20:822–835. doi: 10.1017/S0001867800018395
   Web of Science ®Google Scholar
• Silva M, Oliveira V. Difference equations for the higher order moments and cumulants of the INAR(1) model. J Time Ser Anal. 2004;25:317–333. doi: 10.1111/j.1467-9892.2004.01685.x
   Web of Science ®Google Scholar
• Steutel FW, Van Harn K. Discrete analogues of self-decomposability and stability. Ann Probab. 1979;7:893–899. doi: 10.1214/aop/1176994950
   Web of Science ®Google Scholar
• Weiß C. Thinning operations for modelling time series of counts–a survey. AStA Adv Stat Anal. 2008;92(3):319–341. doi: 10.1007/s10182-008-0072-3
   Web of Science ®Google Scholar
• Wedderburn R. Quasi-likelihood functions, generalized linear models, and the Gauss-Newton method. Biometrika. 1974;61(3):439–447.
   Web of Science ®Google Scholar
• Sutradhar B. An overview on regression models for discrete longitudinal responses. Statist Sci. 2003;18(3):377–393. doi: 10.1214/ss/1076102426
   Web of Science ®Google Scholar
• Sutradhar B, Das K. On the efficiency of regression estimators in generalised linear models for longitudinal data. Biometrika. 1999;86:459–465. doi: 10.1093/biomet/86.2.459
   Web of Science ®Google Scholar
• Sutradhar BC, Jowaheer V, Rao RP. Remarks on asymptotic efficient estimation for regression effects in stationary and nonstationary models for panel count data. Braz J Probab Stat. 2014;28(2):241–254. doi: 10.1214/12-BJPS204
   Web of Science ®Google Scholar
• Mamode Khan N, Sunecher Y, Jowaheer V. Analyzing the full BINMA time series process using a robust GQL approach. J Time Ser Econom. 2016;1–12.
   Google Scholar
• Jowaheer V, Sutradhar B. Analysing longitudinal count data with overdispersion. Biometrika. 2002;89:389–399. doi: 10.1093/biomet/89.2.389
   Web of Science ®Google Scholar
• Prentice RL, Zhao LP. Estimating equations for parameters in means and covariances of multivariate discrete and continuous responses. Biometrics. 1991;47:825–839. doi: 10.2307/2532642
   PubMed Web of Science ®Google Scholar
• Mamode Khan N. A robust algorithm for estimating regression and dispersion parameters in non-stationary longitudinally correlated COM-Poisson. J Comput Math. 2016;19(1):25–36.
   Google Scholar
• Yahav I, Shmueli G. On generating multivariate Poisson data in management science applications. Appl Stoch Models Bus Ind. 2011;28(1):91–102. doi: 10.1002/asmb.901
   Web of Science ®Google Scholar
• Mamode Khan N. Use of vector divisions in solving quasi-likelihood equations for a Poisson model. J Stat Comput Simul. 2012;89:1337–1342. doi: 10.1080/00949655.2011.580345
   Web of Science ®Google Scholar
• Statistics Mauritius. Road transport and road traffic accidents statistics. Ministry of Finance and Economic Development; 2016. (Technical Report; 1236).
   Google Scholar