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Some Asymptotic Properties Of The Sample Covariances Of Gaussian Autoregressive Moving‐Average Processes

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  • Boaz Porat

Abstract

. The paper deals with the asymptotic variances of the sample covariances of autoregressive moving average processes. Using state‐space representations and some matrix Lyapunov equation theory, closed‐form expressions are derived for the asymptotic variances of the sample covariances and for the Cramer‐Rao bounds on the process covariances. The main results obtained from these expressions are as follows: For ARMA (p, q) processes with p≥q, the sample covariance of order n is asymptotically efficient if and only if 0 ≤n≤p – q. For ARMA (p, q) processes with p

Suggested Citation

  • Boaz Porat, 1987. "Some Asymptotic Properties Of The Sample Covariances Of Gaussian Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 205-220, March.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:2:p:205-220
    DOI: 10.1111/j.1467-9892.1987.tb00433.x
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    Cited by:

    1. Alessandra Luati & Francesca Papagni & Tommaso Proietti, 2021. "Efficient Nonparametric Estimation of Generalized Autocovariances," CEIS Research Paper 515, Tor Vergata University, CEIS, revised 14 Oct 2021.
    2. A. M. Walker, 1995. "On Results Of Porat Concerning Asymptotic Efficiency Of Sample Covariances Of Gaussian Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 237-248, March.
    3. Boshnakov, Georgi N., 2005. "On the asymptotic properties of multivariate sample autocovariances," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 42-52, January.
    4. Haruo Iwakura & Ryo Okui, 2014. "Asymptotic Efficiency in Factor Models and Dynamic Panel Data Models," KIER Working Papers 887, Kyoto University, Institute of Economic Research.

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