290
Views
6
CrossRef citations to date
0
Altmetric
Original Articles

Estimating the Change Point of Correlated Poisson Count Processes

, , &

References

  • Al-Osh , M. A. , Alzaid , A. A. ( 1987 ). First-order integer-valued autoregressive (INAR(1)) process . Journal of Time Series Analysis , 8 ( 3 ): 261 – 275 .
  • Alzaid , A. , Al-Osh , M. ( 1988 ). First-order integer-valued autoregressive (INAR (1)) process: Distributional and regression properties . Statistica Neerlandica , 42 ( 1 ): 53 – 61 .
  • Brannas , K. , Hellstrom , J. , Nordstorm , J. ( 2002 ). A new approach to modelling and forecasting monthly guest nights in hotels . International Journal of Forecasting , 18 ( 1 ): 19 – 30 .
  • Brannas , K. , Nordstrom , J. ( 2000 ). A bivariate integer valued allocation model for guest nights in hotels and cottages . Umeå Economic Studies 547. Umeå , Sweden : Department of Economics, Umeå University .
  • Cox , D. R. , Miller , H. D. ( 1965 ). The Theory of Stochastic Processes . New York : Chapman and Hall .
  • Davis , R. A. , Dunsmuir , W. T. M. , Wang , Y. ( 1999 ). Modeling time series of count data . In: Ghosh , S. , Ed. Statistics: Textbooks and Monographs . New York : Marcel Dekker , 63 – 114 .
  • Freeland , R. K. , McCabe , B. ( 2005 ). Asymptotic properties of CLS estimators in the Poisson AR(1) model . Statistics & Probability Letters , 73 ( 2 ): 147 – 153 .
  • Gourieroux , C. , Jasiak , J. ( 2004 ). Heterogeneous INAR(1) model with application to car insurance . Insurance: Mathematics and Economics , 34 ( 2 ): 177 – 192 .
  • Jacobs , P. A. , Lewis , P. A. W. ( 1978a ). Discrete time series generated by mixtures. I: Correlational and runs properties . Journal of the Royal Statistical Society. Series B (Methodological) , 40 ( 1 ): 94 – 105 .
  • Jacobs , P. A. , Lewis , P. A. W. ( 1978b ). Discrete time series generated by mixtures II: Asymptotic properties . Journal of the Royal Statistical Society. Series B (Methodological) , 40 ( 2 ): 222 – 228 .
  • Jacobs , P. A. , Lewis , P. A. W. ( 1978c ). Discrete time series generated by mixtures. III. Autoregressive processes (DAR(p)) . Naval Postgraduate School Technical Report, NPS55Lw 73061A . Monterey , CA : Naval Postgraduate School .
  • Jin-Guan , D. , Yuan , L. ( 1991 ). The integer-valued autoregressive (INAR(p)) model . Journal of Time Series Analysis , 12 ( 2 ): 129 – 142 .
  • Jung , R. C. , Kukuk , M. , Liesenfeld , R. ( 2006 ). Time series of count data: modeling, estimation and diagnostics . Computational Statistics & Data Analysis , 51 ( 4 ): 2350 – 2364 .
  • Jung , R. C. , Ronning , G. , Tremayne , A. R. ( 2005 ). Estimation in conditional first order autoregression with discrete support . Statistical Papers , 46 ( 2 ): 195 – 224 .
  • Jung , R. C. , Tremayne , A. R. ( 2006 ). Binomial thinning models for integer time series . Statistical Modelling , 6 ( 2 ): 81 – 96 .
  • Lewis , P. ( 1980 ). Simple models for positive-valued and discrete-valued time series with ARMA correlation structure . In: Krishnaiah , P. R. , Ed. Multivariate Analysis , Amsterdam: North Holland , 151 – 166 .
  • McKenzie , E. ( 1985 ). Some simple models for discrete variate time series . Journal of the American Water Resources Association , 21 ( 4 ): 645 – 650 .
  • McKenzie , E. ( 2003 ). Discrete variate time series . In: Shanbhag , D. N. , Rao , C. R. , Eds. Handbook of Statistics 21, Stochastic Processes: Modeling and Simulation , North-Holland : Amsterdam , 573 – 606 .
  • Pedeli , X. , Karlis , D. ( 2011 ). A bivariate INAR(1) process with application . Statistical Modelling , 11 ( 4 ): 325 – 349 .
  • Perry , M. B. , Pignatiello , J. J. , Simpson , J. R. ( 2006 ). Estimating the change point of a Poisson rate parameter with a linear trend disturbance . Quality and Reliability Engineering International , 22 ( 4 ): 371 – 384 .
  • Ristiæ , M. M. , Nastiæ , A. S. , Bakouch , H. S. ( 2012 ). Estimation in an integer-valued autoregressive process with negative binomial marginals (NBINAR(1)) . Communications in Statistics - Theory and Methods , 41 ( 4 ): 606 – 618 .
  • Samuel , T. R. , Pignatjello , J. J. ( 1998 ). Identifying the time of a change in a Poisson rate parameter . Quality Engineering , 10 ( 4 ): 673 – 681 .
  • Sprott , D. A. (1983). Estimating the parameters of a convolution by maximum likelihood. Journal of the American Statistical Association , 78(382):457–460.
  • Steutel , F. W. , van Harn , K. ( 1979 ). Discrete analogues of self-decomposability and stability . The Annals of Probability , 7 ( 5 ): 893 – 899 .
  • Timmer , D. H. , Pignatiello , J. J. ( 2003 ). Change point estimates for the parameters of an AR(1) process . Quality and Reliability Engineering International , 19 ( 4 ): 355 – 369 .
  • Weiß , C. H. ( 2007 ). Controlling correlated processes of Poisson counts . Quality and Reliability Engineering International , 23 ( 6 ): 741 – 754 .
  • Weiß , C. H. ( 2008 ). Thinning operations for modeling time series of counts—A survey . Advances in Statistical Analysis , 92 ( 3 ): 319 – 341 .
  • Weiß , C. H. ( 2009 ). EWMA monitoring of correlated processes of Poisson counts . Quality Technology & Quantitative Management , 6 ( 2 ): 137 – 153 .
  • Weiß , C. H. ( 2012 ). Fully observed INAR(1) processes . Journal of Applied Statistics , 39 ( 3 ): 581 – 598 .
  • Weiß , C. H. , Testik , M. C. ( 2009 ). CUSUM monitoring of first-order integer-valued autoregressive processes of Poisson counts . Journal of Quality Technology , 41 ( 4 ): 389 – 400 .
  • Yontay , P. , Weiß , C. H. , Testik , M. C. ( 2013 ). A two-sided cumulative sum chart for first-order integer-valued autoregressive processes of Poisson counts . Quality and Reliability Engineering International , 29 ( 1 ): 33 – 42 .

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.