Generalized RCINAR(p) Process with Signed Thinning Operator

References

• Alonso , A. M. , Peña , D. , Romo , J. ( 2002 ). Forecasting time series with sieve bootstrap . Journal of Statistical Planning and Inference 100 : 1 – 11 .
   Web of Science ®Google Scholar
• Ash , R. , Doléans-Dade , C. ( 2000 ). Probability & Measure Theory. , 2nd ed. San Diego : Academic Press .
   Google Scholar
• Bakouch , H. S. , Ristić , M. M. ( 2010 ). Zero truncated Poisson integer-valued AR(1) model . Metrika 72 : 265 – 280 .
   Web of Science ®Google Scholar
• Bélisle , P. , Joseph , L. , MacGibbon , B. , Wolfson , D. , du Berger , R. ( 1998 ). Change-point analysis of neuron spike train data . Biometrics 54 : 113 – 123 .
   PubMed Web of Science ®Google Scholar
• Bökenholt , U. ( 1999 ). An INAR(1) negative multinomial regression model for longitudinal count data . Psychometrika 64 : 53 – 67 .
   Web of Science ®Google Scholar
• Bökenholt , U. ( 2003 ). Analysing state dependences in emotional experiences by dynamic count data models . Journal of the Royal Statistical Society: Series C (Applied Statistics) 52 : 213 – 226 .
   Web of Science ®Google Scholar
• Cardinal , M. , Roy , R. , Lambert , J. ( 1999 ). On the application of integer-valued time series models for the analysis of disease incidence . Statistics in Medicine 18 : 2025 – 2039 .
   PubMed Web of Science ®Google Scholar
• Cui , Y. , Lund , R. ( 2009 ). A new look at time series of counts . Biometrika 96 : 781 – 792 .
   Web of Science ®Google Scholar
• Drost , F. C. , Akker , R. V. , Werker , B. J. ( 2008a ). Local asymptotic normality and efficient estimation for INAR(p) models . Journal of Time Series Analysis 29 : 783 – 801 .
   Web of Science ®Google Scholar
• Drost , F. C. , Akker , R. V. , Werker , B. J. ( 2008b ). Note on integer-valued bilinear time series models . Statistics and Probability Letters 78 : 992 – 996 .
   Web of Science ®Google Scholar
• Drost , F. C. , Akker , R. V. , Werker , B. J. ( 2009 ). Efficient estimation of auto-regression parameters and innovation distributions for semi-parametric integer-valued AR(p) models . Journal of the Royal Statistical Society Series B 71 : 467 – 485 .
   Google Scholar
• Du , J. , Li , Y. ( 1991 ). The integer-valued autoregressive (INAR(p)) model . Journal of Time Series Analysis 12 : 129 – 142 .
   Google Scholar
• Enciso-Mora , V. , Neal , P. , Rao , T. S. ( 2009 ). Efficient order selection algorithms for integer-valued ARMA processes . Journal of Time Series Analysis 30 : 1 – 18 .
   Web of Science ®Google Scholar
• Freeland , R. , McCabe , B. ( 2004a ). Analysis of low count time series data by Poisson autoregression . Journal of Time Series Analysis 25 : 701 – 722 .
   Web of Science ®Google Scholar
• Freeland , R. , McCabe , B. ( 2004b ). Forecasting discrete valued low count time series . International Journal of Forecasting 20 : 427 – 434 .
   Web of Science ®Google Scholar
• Gomes , D. , CantoeCastro , L. ( 2009 ). Generalized integer-valued random coefficient for a first order structure autoregressive (RCINAR) process . Journal of Statistical Planning and Inference 139 : 4088 – 4097 .
   Web of Science ®Google Scholar
• Hall , P. , Heyde , C. C. ( 1980 ). Martingale Limit Theory and Its Application . New York : Academic Press .
   Google Scholar
• Kim , H. Y. , Park , Y. ( 2008 ). A non stationary integer-valued autorgressive model . Statistical Papers 49 : 485 – 502 .
   Web of Science ®Google Scholar
• Klimko , L. A. , Nelson , P. I. ( 1978 ). On conditional least squares estimation for stochastic processes . Annals of Statistics 6 : 629 – 642 .
   Web of Science ®Google Scholar
• Latour , A. (1998). Existence and stochastic structure of a non negative integer-valued autoregressive process. Journal of Time Series Analysis 19:439–455.
   Google Scholar
• McCabe , B. , Martin , G. ( 2005 ). Bayesian predictions of low count time series . International Journal of Forecasting 21 : 315 – 330 .
   Web of Science ®Google Scholar
• Ristić , M. M. , Bakouch , H. B. , Nastić , A. S. ( 2009 ). A new geometric first-order integer-valued autoregressive (NGINAR(1)) process . Journal of Statistical Planning and Inference 139 : 2218 – 2226 .
   Web of Science ®Google Scholar
• Weiß, C. H. ( 2008a ). Serial dependence and regression of Poisson INARMA models . Journal of Statistical Planning and Inference 138 : 2975 – 2990 .
   Web of Science ®Google Scholar
• Weiß, C. H. ( 2008b ). Thinning operations for modeling time series of counts—a survey . Advances in Statistical Analysis 92 : 319 – 343 .
   Web of Science ®Google Scholar
• Zhang , H. , Wang , D. , Zhu , F. ( 2010a ). Empirical likelihood for first-order random coefficient integer-valued autoregressive processes . Communications in Statistics: Theory and Methods . doi: DOI: 10.1080103610920903443997
   Web of Science ®Google Scholar
• Zhang , H. , Wang , D. , Zhu , F. ( 2010b ). Inference for INAR(p) processes with signed generalized power series thinning operator . Journal of Statistical Planning and Inference 140 : 667 – 683 .
   Web of Science ®Google Scholar
• Zheng , H. , Basawa , I. V. , Datta , S. ( 2006 ). Inference for pth-order random coefficient integer-valued autoregressive processes . Journal of Time Series Analysis 27 : 411 – 440 .
   Web of Science ®Google Scholar
• Zheng , H. , Basawa , I. V. , Datta , S. ( 2007 ). First-order random coefficient integer-valued autoregressive processes . Journal of Statistical Planning and Inference 137 : 212 – 229 .
   Web of Science ®Google Scholar
• Zheng , H. , Basawa , I. V. ( 2008 ). First-order observation-driven integer-valued autoregressive processes . Statistics and Probability Letters 78 : 1 – 9 .
   Web of Science ®Google Scholar