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Rate Of Convergence Of Centred Estimates Of Autoregressive Parameters For Infinite Variance Autoregressions

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  • Keith Knight

Abstract

. Let Yn=μ+Σβj (Yn–j–μ) +ɛn be a pth order autoregressive process with innovations {ɛn} in the domain of attraction of a stable law with index α α. It is shown here that if α is estimated by the sample mean, N1/δ(βj–βj) → O almost surely for δ > max(1, α). In addition, some statements are made regarding estimators of α which will give the full (Hannan and Kanter) rate of convergence, in particular when α

Suggested Citation

  • Keith Knight, 1987. "Rate Of Convergence Of Centred Estimates Of Autoregressive Parameters For Infinite Variance Autoregressions," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(1), pages 51-60, January.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:1:p:51-60
    DOI: 10.1111/j.1467-9892.1987.tb00420.x
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    Cited by:

    1. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility Regressions with Fat Tails," TSE Working Papers 20-1097, Toulouse School of Economics (TSE).
    2. Kim, Jihyun & Meddahi, Nour, 2020. "Volatility regressions with fat tails," Journal of Econometrics, Elsevier, vol. 218(2), pages 690-713.
    3. Zhu, Ke & Ling, Shiqing, 2013. "Global self-weighted and local quasi-maximum exponential likelihood estimators for ARMA-GARCH/IGARCH models," MPRA Paper 51509, University Library of Munich, Germany.
    4. Bouhaddioui, Chafik & Ghoudi, Kilani, 2012. "Empirical processes for infinite variance autoregressive models," Journal of Multivariate Analysis, Elsevier, vol. 107(C), pages 319-335.
    5. Ke Zhu & Shiqing Ling, 2015. "LADE-Based Inference for ARMA Models With Unspecified and Heavy-Tailed Heteroscedastic Noises," Journal of the American Statistical Association, Taylor & Francis Journals, vol. 110(510), pages 784-794, June.
    6. Jihyun Kim & Nour Meddahi, 2020. "Volatility Regressions with Fat Tails," Post-Print hal-03142647, HAL.
    7. Christis Katsouris, 2022. "Asymptotic Theory for Unit Root Moderate Deviations in Quantile Autoregressions and Predictive Regressions," Papers 2204.02073, arXiv.org, revised Aug 2023.

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