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Goodness-of-fit for a branching process with immigration using sample partial autocorrelations

Author

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  • Mills, T. M.
  • Seneta, E.

Abstract

A limit theorem is developed for sample partial autocorrelations, when the vector {N1/2(R(k)-mk), K=1,...,H} converges in distribution, the R(k) being sample autocorrelations from a not-necessarily stationary process. The result is used to develop a Quenouille-type goodness-of-fit test based on sample partial autocorrelations for the simple branching process with immigration. This is compared with a test of Venkataraman (1982); and both are applied to historical data.

Suggested Citation

  • Mills, T. M. & Seneta, E., 1989. "Goodness-of-fit for a branching process with immigration using sample partial autocorrelations," Stochastic Processes and their Applications, Elsevier, vol. 33(1), pages 151-161, October.
    • Handle: RePEc:eee:spapps:v:33:y:1989:i:1:p:151-161
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    Citations

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    Cited by:

    1. Tianqing Liu & Xiaohui Yuan, 2013. "Random rounded integer-valued autoregressive conditional heteroskedastic process," Statistical Papers, Springer, vol. 54(3), pages 645-683, August.
    2. Ku, Simon F., 1997. "Limited distribution of sample partial autocorrelations: A matrix approach," Stochastic Processes and their Applications, Elsevier, vol. 72(1), pages 121-143, December.
    3. Jung, Robert C. & Tremayne, A.R., 2006. "Coherent forecasting in integer time series models," International Journal of Forecasting, Elsevier, vol. 22(2), pages 223-238.
    4. Simon Ku & Eugene Seneta, 1996. "Quenouille-type theorem on autocorrelations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(4), pages 621-630, December.

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