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Limited distribution of sample partial autocorrelations: A matrix approach

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  • Ku, Simon F.

Abstract

We develop a technique for derivation of the asymptotic joint distribution of the sample partial autocorrelations of a process, given the corresponding distribution of sample autocorrelations. No assumption of asymptotic normality is needed. The underlying process need not be stationary. The technique is demonstrated through a detailed study of ARMA (1,1)-like processes, but is applicable to other models. The results extend those of Mills and Seneta (1989) for the AR(1)-like case. The study is motivated by the known relationships and properties, especially is the classical AR(p) case, of population and sample partial autocorrelations.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:spapps:v:72:y:1997:i:1:p:121-143
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Barndorff-Nielsen, O. & Schou, G., 1973. "On the parametrization of autoregressive models by partial autocorrelations," Journal of Multivariate Analysis, Elsevier, vol. 3(4), pages 408-419, December.
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