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Statistics
A Journal of Theoretical and Applied Statistics
Volume 45, 2011 - Issue 1: Statistics on Dependent Data
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Original Articles

Some recent progress in count time series

Pages 49-58 | Received 26 Jun 2010, Published online: 06 Feb 2011

References

  • Bollerslev , T. 1986 . Generalized autoregressive conditional heteroskedasticity . J. Econometrics , 31 : 307 – 327 .
  • McCullagh , P. and Nelder , J. A. 1989 . Generalized Linear Models , 2 , London : Chapman & Hall .
  • Kedem , B. and Fokianos , K. 2002 . Regression Models for Time Series Analysis , Hoboken, NJ : Wiley .
  • Al-Osh , M. A. and Alzaid , A. A. 1987 . First-order integer-valued autoregressive (INAR(1)) process . J. Time Ser. Anal. , 8 : 261 – 275 .
  • Du , J. G. and Li , Y. 1991 . The integer-valued autoregressive INAR (p) model . J. Time Ser. Anal. , 12 : 129 – 142 .
  • Joe , H. 1997 . Multivariate Models and Dependence Concepts , London : Chapman & Hall .
  • Latour , A. 1998 . Existence and stochastic structure of a non-negative integer-valued autoregressive process . J. Time Ser. Anal. , 19 : 439 – 455 .
  • Doukhan , P. , Latour , A. and Oraichi , D. 2006 . A simple integer-valued bilinear time series model . Adv. Appl. Probab. , 38 : 559 – 578 .
  • Bu , R. , McCabe , B. and Hadri , K. 2008 . Maximum likelihood estimation of higher-order integer-valued autoregressive process . J. Time Ser. Anal. , : 973 – 994 .
  • Drost , F. C. , van den Akker , R. and Werker , B. J.M. 2009 . Efficient estimation of autoregression parameters and innovation distributions for semiparametric integer-valued AR(p) models . J. R. Stat. Soc. Ser. B , 71 : 467 – 485 .
  • McKenzie , E. 2003 . “ Discrete variate time series ” . In Stochastic Processes: Modelling and Simulation, Handbook of Statist , Edited by: Shanbag , D. N. and Rao , C. R. Vol. 21 , 573 – 606 . Amsterdam : North-Holland .
  • Weiß , C. H. 2008 . Thinning operations for modeling time series of counts – a survey . AStA Adv. Statist. Anal. , 92 : 319 – 341 .
  • Cox , D. R. 1981 . Statistical analysis of time series: Some recent developments . Scand. J. Statist. , 8 : 93 – 115 .
  • Zeger , S. L. 1988 . A regression model for time series of counts . Biometrika , 75 : 621 – 629 .
  • Harvey , A. C. and Fernandes , C. 1989 . Time series models for count or qualitative observations . J. Bus. Econom. Statist. , 7 : 407 – 422 . (with discussion)
  • MacDonald , I. L. and Zucchini , W. 1997 . Hidden Markov and Other Models for Discrete-valued Time Series , London : Chapman & Hall .
  • Davis , R. and Wu , R. 2009 . A negative binomial model for time series of counts . Biometrika , 96 : 735 – 749 .
  • Cui , Y. and Lund , R. 2009 . A new look at time series of counts . Biometrika , 96 : 781 – 792 .
  • Brockwell , P. J. and Davis , R. A. 1991 . Time Series: Data Analysis and Theory , 2 , New York : Springer .
  • Zeger , S. L. and Qaqish , B. 1988 . Markov regression models for time series: A quasi-likelihood approach . Biometrics , 44 : 1019 – 1031 .
  • Li , W. K. 1994 . Time series models based on generalized linear models: Some further results . Biometrics , 50 : 506 – 511 .
  • Brumback , B. A. , Ryan , L. M. , Schwartz , J. D. , Neas , L. M. , Stark , P. C. and Burge , H. A. 2000 . Transitional regression models with application to environmental time series . J. Amer. Statist. Assoc. , 85 : 16 – 27 .
  • Fokianos , K. 2001 . Truncated Poisson regression for time series of counts . Scand. J. Statist. , 28 : 645 – 659 .
  • Fahrmeir , L. and Tutz , G. 2001 . Multivariate Statistical Modelling Based on Generalized Linear Models , 2 , New York : Springer .
  • Davis , R. A. , Dunsmuir , W. T.M. and Streett , S. B. 2003 . Observation-driven models for Poisson counts . Biometrika , 90 : 777 – 790 .
  • Fokianos , K. and Kedem , B. 2004 . Partial likelihood inference for time series following generalized linear models . J. Time Ser. Anal. , 25 : 173 – 197 .
  • Jung , R. C. , Kukuk , M. and Liesenfeld , R. 2006 . Time series of count data: Modeling, estimation and diagnostics . Comput. Statist. Data Anal. , 51 : 2350 – 2364 .
  • Davis , R. A. , Wang , Y. and Dunsmuir , W. T.M. 1999 . “ Modelling time series of count data ” . In Asymptotics, Nonparametric & Time Series , Edited by: Ghosh , S. 63 – 114 . New York : Marcel Dekker .
  • Jørgensen , B. 1997 . The Theory of Dispersion Models , London : Chapman & Hall .
  • Zhu , F. 2011 . A negative binomial integer-valued GARCH model . J. Time Series Anal. , preprint. Available at http://dx.doi.org/10.1111/j.1467-9892.2010.00684.x
  • Wong , W. H. 1986 . Theory of partial likelihood . Ann. Statist. , 14 : 88 – 123 .
  • Slud , E. V. and Kedem , B. 1994 . Partial likelihood analysis of logistic regression and autoregression . Statist. Sinica , 4 : 89 – 106 .
  • Fokianos , K. and Kedem , B. 1998 . Prediction and classification of non-stationary categorical time series . J. Multivariate Anal. , 67 : 277 – 296 .
  • Fokianos , K. , Rahbek , A. and Tjøstheim , D. 2009 . Poisson autoregression . J. Amer. Statist. Assoc. , 104 : 1430 – 1439 .
  • Zhu , F. and Wang , D. 2009 . Estimation and testing for a Poisson autregressive model . Metrika , preprint. doi:10.1007/s00184-009-0274-z
  • Rydberg , T. H. and Shephard , N. 2000 . “ A modeling framework for the prices and times of trades on the New York stock exchange ” . In Nonlinear and Nonstationary Signal Processing , Edited by: Fitzgerald , W. J. , Smith , R. L. , Walden , A. T. and Young , P. C. 217 – 246 . Cambridge : Isaac Newton Institute and Cambridge University Press .
  • Streett , S. 2000 . “ Some observation driven models for time series of counts ” . Colorado State University, Department of Statistics . Ph.D. thesis
  • Heinen , A. 2003 . “ Modelling time series count data: An autoregressive conditional poisson model ” . Germany : University Library of Munich . Tech. Rep. MPRA Paper 8113 Available at http://mpra.ub.uni-muenchen.de/8113/
  • Ferland , R. , Latour , A. and Oraichi , D. 2006 . Integer-valued GARCH processes . J. Time Ser. Anal. , 27 : 923 – 942 .
  • Fokianos , K. and Tjøstheim , D. 2011 . Log-linear Poisson autoregression . J. Multivariate Anal , preprint
  • Haggan , V. and Ozaki , T. 1981 . Modelling nonlinear random vibrations using an amplitude-dependent autoregressive time series model . Biometrika , 68 : 189 – 196 .
  • Teräsvirta , T. , Tjøstheim , D. and Granger , C. W.J. 2011 . Nonlinear Econometric Modelling , Oxford : Oxford University Press . to appear
  • Tong , H. 1990 . Nonlinear Time Series:A Dynamical System Approach , New York : Oxford University Press .
  • Fan , J. and Yao , Q. 2003 . Nonlinear Time Series , New York : Springer-Verlag .
  • Neumann , M. 2010 . Poisson count processes: Ergodicity and goodness-of-fit . Bernoulli , preprint
  • Franke , J. 2010 . Weak dependence of functional INGARCH processes . unpublished manuscript
  • Doukhan , P. and Louhichi , S. 1999 . A new weak dependence condition and applications to moment inequalities . Stochastic Process. Appl. , 84 : 313 – 342 .
  • Dedecker , J. , Doukhan , P. , Lang , G. , León , J. R. , Louhichi , R. S. and Prieur , C. 2007 . Weak Dependence: With Examples and Applications , New York : Springer . Volume 190 of Lecture Notes in Statistics
  • Heyde , C. C. 1997 . Quasi-Likelihood and its Applications: A General Approach to Optimal Parameter Estimation , New York : Springer .
  • Berkes , I. , Horváth , L. and Kokoszka , P. 2003 . GARCH processes: Structure and estimation . Bernoulli , 9 : 201 – 227 .
  • Fokianos , K. and Tjøstheim , D. 2010 . Nonlinear Poisson autoregression . submitted for publication
  • Davis , R. A. , Dunsmuir , W. T.M. and Streett , S. B. 2005 . Maximum likelihood estimation for an observation driven model for Poisson counts . Methodol. Comput. Appl. Probab , 7 : 149 – 159 .
  • Cox , D. R. 1975 . Partial likelihood . Biometrika , 62 : 69 – 76 .
  • Billingsley , P. 1961 . Statistical Inference for Markov Processes , Chicago : University of Chicago Press .
  • Meyn , S. P. and Tweedie , R. L. 1993 . Markov Chains and Stochastic Stability , London : Springer .
  • Nelder , J. A. and Wedderburn , R. W.M. 1972 . Generalized linear models . J. R. Stat. Soc. Ser. A , 135 : 370 – 384 .

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