100
Views
10
CrossRef citations to date
0
Altmetric
INFERENCE

Optimal Alarm Systems for Count Processes

, &
Pages 3054-3076 | Received 20 Jun 2007, Accepted 26 Mar 2008, Published online: 15 Aug 2008

References

  • Ahn , S. , Gyemin , L. , Jongwoo , J. ( 2000 ). Analysis of the M/D/1-type queue based on an integer-valued autoregressive process . Oper. Res. Lett. 27 : 235 – 241 .
  • Al-Osh , M. A. , Alzaid , A. A. ( 1987 ). First order integer-valued autoregressive INAR(1) process . J. Time Ser. Anal. 8 : 261 – 275 .
  • Al-Osh , M. , Alzaid , A. ( 1988 ). Integer-valued moving average (INMA) process . Statist. Pap. 29 : 281 – 300 .
  • Aly , E.-E. , Bouzar , N. ( 1994 ). Explicit stationary distributions for some Galton-Watson processes with immigration . Commun. Statist. Stochastic Mod. 10 : 499 – 517 .
  • Aly , E.-E. , Bouzar , N. ( 2005 ). Stationary solutions for integer-valued autoregressive processes . Int. J. Math. Math. Sci. 1 : 1 – 18 .
  • Amaral-Turkman , M. A. , Turkman , K. F. ( 1990 ). Optimal alarm systems for autoregressive processes; a Bayesian approach . Comput. Statist. Data Anal. 10 : 307 – 314 .
  • Antunes , M. ( 2002 ). Some Problems in Non-Linear Prediction . Unpublished doctoral dissertation, University of Lisbon, Lisbon, Portugal .
  • Antunes , M. , Amaral-Turkman , M. A. , Turkman , K. F. (2003). A Bayesian approach to event prediction intervals. J. Time Ser. Anal. 24:631–646.
  • Blundell , R. , Griffith , R. , Windmeijer , F. ( 2002 ). Individual effects and dynamics in count data models . J. Econometrics 108 : 113 – 131 .
  • Braga , A. L. , Zanobetti , A. , Schwartz , J. ( 2001 ). The time course of weather-related deaths . Epidemiology 12 : 662 – 667 .
  • Brännäs , K. ( 1995 ). Explanatory variables in the AR(1) count data model . Umeå Econ. Stud. 381 .
  • Brännäs , K. , Hall , A. ( 2001 ). Estimation in integer-valued moving average models . Appl. Stochastic Mod. Bus. Ind. 17 : 277 – 291 .
  • Brännäs , K. , Hellström , J. ( 2001 ). Generalized integer-valued autoregression . Econometric Rev. 20 : 425 – 443 .
  • Brännäs , K. , Hellström , J. , Nordström , J. ( 2002 ). A new approach to modelling and forecasting monthly guest nights in hotels . Int. J. Forecast. 18 : 9 – 30 .
  • Brännäs , K. , Nordström , J. ( 2004 ). An integer-valued time series model for hotels that accounts for constrained capacity . Stud. Nonlinear Dyn. Econometrics 8 : 4 , article 6 .
  • Brännäs , K. , Nordström , J. ( 2006 ). Tourist accomodation effects of festivals . Tourism Econ. 12 : 291 – 302 .
  • Campbell , M. J. , Julious , S. A. , Peterson , C. K. , Tobias , A. ( 2001 ). Atmospheric pressure and sudden infant death syndrome in Cook County, Chicago . Paediatr Perinat Epidemiol. 15 : 287 – 289 .
  • de Maré , J. ( 1980 ). Optimal prediction of catastrophes with application to Gaussian process . Ann. Probab. 8 : 841 – 850 .
  • Du , J.-G. , Li , Y. ( 1991 ). The integer valued autoregressive (INAR(p)) model . J. Time Ser. Anal. 12 : 129 – 142 .
  • Garcia-Ferrer , A. , Queralt , R. A. ( 1997 ). A note on forecasting international tourism deman in Spain . Int. J. Forecast. 13 : 539 – 549 .
  • Katsouyanni , K. , Touloumi , G. , Samoli , E. , Gryparis , A. , Le Tertre , A. , Monopolis , Y. , Rossi , G. ( 2002 ). Confounding and effect modification in the short-term effects of ambient particles on total mortality: results from 29 European cities within the APHEA 2 project . Epidemiology 12 : 521 – 531 .
  • Koop , G. , Tale , L. ( 2004 ). Measuring the health effects of air pollution: to what extent can we really say that people are dying from bad air? J. Environ. Econ. Manage. 47 : 30 – 54 .
  • Latour , A. ( 1988 ). Existence and stochastic structure of a non-negative integer-valued autoregressive processes . J. Time Ser. Anal. 4 : 439 – 455 .
  • Lindgren , G. ( 1975a ). Prediction for a random point time . Ann. Probab. 3 : 412 – 423 .
  • Lindgren , G. ( 1975b ). Prediction of catastrophes and high level crossings . Bull. Int. Statist. Inst. 46 : 225 – 240 .
  • Lindgren , G. ( 1980 ). Model processes in non-linear prediction, with application to detection and alarm . Ann. Probab. 8 : 775 – 792 .
  • Lindgren , G. ( 1985 ). Optimal prediction of level crossings in Gaussian processes and sequences . Ann. Probab. 13 : 804 – 824 .
  • McCabe , B. P. M. , Martin , G. M. ( 2005 ). Bayesian prediction of low count time series . Int. J. Forecast. 21 : 315 – 330 .
  • McKenzie , E. ( 1985 ). Some simple models for discrete variate time series . Water Res. Bull. 21 : 645 – 650 .
  • McKenzie , E. ( 2003 ). Discrete variate time series . In: Shanbhag , D. N. , Rao , C. R. , eds. Handbook of Statistics . Amsterdam : Elsevier Science , pp. 573 – 606 .
  • Neal , P. , Subba Rao , T. ( 2007 ). MCMC for integer-valued ARMA processes . J. Time Ser. Anal. 28 : 92 – 110 .
  • Nordström , J. ( 1996 ). Tourism satellite account for Sweden 1992–93 . Tourism Econ. 2 : 13 – 42 .
  • Quoreshi , A. M. M. S. ( 2006 ). Bivariate time series modelling of financial count data . Commun. Statist. Theor. Meth. 35 : 1343 – 1358 .
  • Schwartz , J. , Levin , R. , Hodge , K. (1997). Drinking water turbidity and paediatric hospital use for gastrointestinal illness in Philadelphia. Epidemiology 8:615–620.
  • Silva , M. E. , Oliveira , V. L. ( 2004 ). Difference equations for the higher-order moments and cumulants of the INAR(1) model . J. Time Ser. Anal. 25 : 317 – 333 .
  • Silva , I. , Silva , M. E. , Pereira , I. , Silva , N. ( 2005 ). Replicated INAR(1) processes . Methodol. Comput. Appl. Probab. 7 : 517 – 542 .
  • Svensson , A. , Lindquist , R. , Lindgren , G. ( 1996 ). Optimal prediction of catastrophes in autoregressive moving average processes . J. Time Ser. Anal. 17 : 511 – 531 .
  • Svensson , A. , Holst , J. ( 1997 ). Optimal prediction of level-crossing in piecewise linear Gaussian processes with changing catastrophe level . Technical Report 1997:14, Department of Mathematical Statistics, Lund Institute of Technology .
  • Svensson , A. , Holst , J. ( 1998 ). Prediction of the high water levels in the Baltic . Istatistik J. Turkish Statist. Assoc. 1 : 39 – 46 .
  • Tanner , M. A. ( 1996 ). Tools for Statistical Inference: Methods for Exploration of Posterior Distributions and Likelihood Functions. , 3rd ed. New-York : Springer-Verlag .
  • Touloumi , G. , Atkinson , R. , Le Tertre , A. , Samoli , E. , Schwartz , J. , Schlinder , C. , Vonk , J. M. , Rossi , G. , Saez , M. , Rabszenko , D. , Katsouyanni , K. ( 2004 ). Analysis of health outcome time series data in epidemiological studies . Environmetrics 15 : 101 – 117 .
  • Zheng , H. T. , Basawa , I. V. , Datta , S. ( 2006 ). Inference for pth-order random coefficient integer-valued autoregressive processes . J. Time Ser. Anal. 27 : 411 – 440 .
  • Zheng , H. T. , Basawa , I. V. , Datta , S. ( 2007 ). First-order random coefficient integer-valued autoregressive processes . J. Statist. Plann. Infer. 173 : 212 – 229 .
  • Zhou , J. , Basawa , I. V. ( 2005 ). Least-squared estimation for bifurcation autoregressive processes . Statist. Probab. Lett. 74 : 77 – 88 .
  • Zhu , R. , Joe , H. ( 2003 ). A new type of discrete self-decomposability and its applications to continuous-time Markov processes for modeling count data time series . Stoch. Mod. 19 : 235 – 254 .

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.