# Binomial ARMA count series from renewal processes

Discussiones Mathematicae Probability and Statistics (2012)

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

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topSergiy 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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