Binomial ARMA count series from renewal processes

Sergiy Koshkin; Yunwei Cui

Discussiones Mathematicae Probability and Statistics (2012)

  • Volume: 32, Issue: 1-2, page 5-16
  • ISSN: 1509-9423

Abstract

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This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.

How to cite

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Sergiy Koshkin, and Yunwei Cui. "Binomial ARMA count series from renewal processes." Discussiones Mathematicae Probability and Statistics 32.1-2 (2012): 5-16. <http://eudml.org/doc/270965>.

@article{SergiyKoshkin2012,
abstract = {This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.},
author = {Sergiy Koshkin, Yunwei Cui},
journal = {Discussiones Mathematicae Probability and Statistics},
keywords = {integer-valued time series; stochastic difference equations; autoregressive moving average; renewal process; lifetime distribution; probability generating function; palindromic polynomial; constant hazard rate},
language = {eng},
number = {1-2},
pages = {5-16},
title = {Binomial ARMA count series from renewal processes},
url = {http://eudml.org/doc/270965},
volume = {32},
year = {2012},
}

TY - JOUR
AU - Sergiy Koshkin
AU - Yunwei Cui
TI - Binomial ARMA count series from renewal processes
JO - Discussiones Mathematicae Probability and Statistics
PY - 2012
VL - 32
IS - 1-2
SP - 5
EP - 16
AB - This paper describes a new method for generating stationary integer-valued time series from renewal processes. We prove that if the lifetime distribution of renewal processes is nonlattice and the probability generating function is rational, then the generated time series satisfy causal and invertible ARMA type stochastic difference equations. The result provides an easy method for generating integer-valued time series with ARMA type autocovariance functions. Examples of generating binomial ARMA(p,p-1) series from lifetime distributions with constant hazard rates after lag p are given as an illustration.
LA - eng
KW - integer-valued time series; stochastic difference equations; autoregressive moving average; renewal process; lifetime distribution; probability generating function; palindromic polynomial; constant hazard rate
UR - http://eudml.org/doc/270965
ER -

References

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  7. [7] R.A. Davis and R. Wu, A negative binomial model for time series of counts, Biometrika 96 (2009) 735-749. doi: 10.1093/biomet/asp029 Zbl1170.62062
  8. [8] An Introduction to Probability Theory and Its Applications, Volume I (3rd ed., Wiley, New York, 1968). 
  9. [9] Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, New York, 1968). 
  10. [10] E. McKenzie, Discrete variate time series, in: Stochastic Processes: Modelling and Simulation, Handbook of Statistics, 21, D.N. Shanbhag and C.R. Rao (Ed(s)), (North-Holland, Amsterdam, 1999) 573-606 
  11. [11] Spectral Analysis and Time Series (Academic Press, London, 1981). 
  12. [12] Stochastic Processes (2nd ed., Wiley, New York, 1995). 
  13. [13] First-order random coefficient integer-valued autoregressive processes, Journal of Statistical Planning and Inference 173 (2007) 212-229. doi: 10.1016/j.jspi.2005.12.003 Zbl1098.62117

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