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On The Asymptotic Distribution Of The Generalized Partial Autocorrelation Function In Autoregressive Moving‐Average Processes

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  • Byoung Seon Choi

Abstract

. It has been conjectured and illustrated that the estimate of the generalized partial autocorrelation function (GPAC), which has been used for the identification of autoregressive moving‐average (ARMA) models, has a thick‐tailed asymptotic distribution. The purpose of this paper is to investigate the asymptotic behaviour of the GPAC in detail. It will be shown that the GPAC can be represented as a ratio of two functions, known as the θ function and the Λ function, each of which itself has a useful pattern for ARMA model identification. We shall show the consistencies of the extended Yule‐Walker estimates of the three functions and present their asymptotic distributions.

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  • Byoung Seon Choi, 1991. "On The Asymptotic Distribution Of The Generalized Partial Autocorrelation Function In Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 12(3), pages 193-205, May.
    • Handle: RePEc:bla:jtsera:v:12:y:1991:i:3:p:193-205
    DOI: 10.1111/j.1467-9892.1991.tb00077.x
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    Cited by:

    1. Yi, Seongbaek, 2005. "The asymptotic distribution of the constant behavior of the generalized partial autocorrelation function of an ARMA process," Statistics & Probability Letters, Elsevier, vol. 75(2), pages 113-118, November.
    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. Choi, ByoungSeon, 1997. "A recursive algorithm for solving the spatial Yule-Walker equations of causal spatial AR models," Statistics & Probability Letters, Elsevier, vol. 33(3), pages 241-251, May.

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