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Threshold Models for Integer-Valued Time Series with Infinite or Finite Range

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Stochastic Models, Statistics and Their Applications

Part of the book series: Springer Proceedings in Mathematics & Statistics ((PROMS,volume 122))

Abstract

Threshold models are very popular in research and application. We survey threshold models for integer-valued time series with an infinite range and compare two of them in a real data example. In particular, we propose and briefly discuss two new models for count data time series with a finite range.

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Notes

  1. 1.

    The authors call their model self-excited, but to have a consistent notation the name is changed.

References

  1. Chen CWS, So MKP, Liu F-C (2011) A review of threshold time series models in finance. Stat Interface 4:167–181

    Article  MathSciNet  MATH  Google Scholar 

  2. Douc R, Doukhan P, Moulines E (2012) Ergodicity of observation-driven time series models and consistency of the maximum likelihood estimator. Stoch Process Appl 123(7):2473–2920

    MathSciNet  Google Scholar 

  3. Ferland R, Latour A, Oraichi D (2006) Integer-valued GARCH process. J Time Ser Anal 27(6):923–942

    Article  MathSciNet  MATH  Google Scholar 

  4. Hansen BE (2011) Threshold autoregression in economics. Stat Interface 4:123–127

    Article  MathSciNet  Google Scholar 

  5. McKenzie E (1985) Some simple models for discrete variate time series. J Am Water Resour Assoc 21(4):645–650

    Article  MathSciNet  Google Scholar 

  6. Monteiro M, Scotto MG, Pereira I (2012) Integer-valued self-exciting threshold autoregressive processes. Commun Stat, Theory Methods 41(15):2717–2737

    Article  MathSciNet  MATH  Google Scholar 

  7. Pakes AG (1971) A branching process with a state dependent immigration component. Adv Appl Probab 3(2):301–314

    Article  MathSciNet  MATH  Google Scholar 

  8. Steutel FW, van Harn K (1979) Discrete analogues of self-decomposability and stability. Ann Probab 7(5):893–899

    Article  MathSciNet  MATH  Google Scholar 

  9. Thyregod P, Carstensen J, Madsen H, Arnbjerg-Nielsen K (1999) Integer valued autoregressive models for tipping bucket rainfall measurements. Environmetrics 10:395–411

    Article  MATH  Google Scholar 

  10. Tong H (2011) Threshold models in time series analysis – 30 years on. Stat Interface 4:107–118

    Article  MathSciNet  MATH  Google Scholar 

  11. Tong H, Lim KS (1980) Threshold autoregression, limit cycles and cyclical data. J R Stat Soc, Ser B, Stat Methodol 42(3):245–292

    MATH  Google Scholar 

  12. Wang C, Liu H, Yao JF, Davis RA, Li WK (2014) Self-excited threshold Poisson autoregression. J Am Stat Assoc 109(506):777–787

    Article  MathSciNet  Google Scholar 

  13. Watier L, Richardson S (1995) Modelling of an epidemiological time series by a threshold autoregressive model. Statistician 44(3):353–364

    Article  Google Scholar 

  14. Weiß CH, Pollett PK (2014) Binomial autoregressive processes with density-dependent thinning. J Time Ser Anal 35(2):115–132

    Article  MATH  Google Scholar 

  15. Woodard DB, Matteson DS, Henderson SG (2011) Stationarity of generalized autoregressive moving average models. Electron J Stat 5:800–828

    Article  MathSciNet  MATH  Google Scholar 

  16. Yu K, Zou H, Shi D (2014) Integer-valued moving average models with structural changes. Mathematical problems in engineering 2014

    Google Scholar 

  17. Zucchini W, MacDonald IL (2009) Hidden Markov models for time series: an introduction using R. CRC Press, Boca Raton

    Book  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Mathematics and Statistics, Helmut Schmidt University, 22008, Hamburg, Germany

    Tobias Möller & Christian H. Weiß

Authors
  1. Tobias Möller
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  2. Christian H. Weiß
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Corresponding author

Correspondence to Tobias Möller .

Editor information

Editors and Affiliations

  1. Institute of Statistics, RWTH Aachen University, Aachen, Germany

    Ansgar Steland

  2. Dept. of Computer Engineering, Control and Robotics, Wrocław University of Technology, Wrocław, Poland

    Ewaryst Rafajłowicz

  3. Inst. of Mathematics and Computer Science, Wrocław University of Technology, Wrocław, Poland

    Krzysztof Szajowski

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Möller, T., Weiß, C.H. (2015). Threshold Models for Integer-Valued Time Series with Infinite or Finite Range. In: Steland, A., Rafajłowicz, E., Szajowski, K. (eds) Stochastic Models, Statistics and Their Applications. Springer Proceedings in Mathematics & Statistics, vol 122. Springer, Cham. https://doi.org/10.1007/978-3-319-13881-7_36

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