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2012 | 32 | 1-2 | 5-16
Tytuł artykułu

Binomial ARMA count series from renewal processes

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Języki publikacji
EN
Abstrakty
EN
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.
Twórcy
  • Computer and Mathematical Sciences Department, University of Houston Downtown, Houston, TX 77002, USA
autor
  • Computer and Mathematical Sciences Department, University of Houston Downtown, Houston, TX 77002, USA
Bibliografia
  • [1] Time Series: Theory and Methods (Springer, New York, 1991). doi: 10.1007/978-1-4419-0320-4
  • [2] Time series formed from the superposition of discrete renewal processes, Journal of Applied Probability 26 (1989) 189-195. doi: 10.2307/3214330
  • [3] Some properties and a characterization of trivariate and multivariate binomial distributions , Statistics 36 (2002) 211-218. doi: 10.1080/02331880212859
  • [4] A new look at time series of counts , Biometrika 96 (2009) 781-792. doi: 10.1093/biomet/asp057
  • [5] Inference in binomial AR(1) models, Statistics and Probability Letters 80 (2010) 1985-1990. doi: 10.1016/j.spl.2010.09.003
  • [6] On the superposition of renewal processes , Biometrika 41 (1954) 91-99
  • [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
  • [8] An Introduction to Probability Theory and Its Applications, Volume I (3rd ed., Wiley, New York, 1968).
  • [9] Limit Distributions for Sums of Independent Random Variables (Addison-Wesley, New York, 1968).
  • [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] Spectral Analysis and Time Series (Academic Press, London, 1981).
  • [12] Stochastic Processes (2nd ed., Wiley, New York, 1995).
  • [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
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-doi-10_7151_dmps_1140
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