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Least absolute deviation estimation for general autoregressive moving average time-series models

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  • Rongning Wu
  • Richard A. Davis
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    Abstract

    We study least absolute deviation (LAD) estimation for general autoregressive moving average time-series models that may be noncausal, noninvertible or both. For ARMA models with Gaussian noise, causality and invertibility are assumed for the parameterization to be identifiable. The assumptions, however, are not required for models with non-Gaussian noise, and hence are removed in our study. We derive a functional limit theorem for random processes based on an LAD objective function, and establish the consistency and asymptotic normality of the LAD estimator. The performance of the estimator is evaluated via simulation and compared with the asymptotic theory. Application to real data is also provided. Copyright Copyright 2010 Blackwell Publishing Ltd

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9892.2009.00648.x
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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Journal of Time Series Analysis.

    Volume (Year): 31 (2010)
    Issue (Month): 2 (03)
    Pages: 98-112

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    Handle: RePEc:bla:jtsera:v:31:y:2010:i:2:p:98-112

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    Web page: http://www.blackwellpublishing.com/journal.asp?ref=0143-9782

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    Cited by:
    1. Lanne, Markku & Meitz, Mika & Saikkonen, Pentti, 2012. "Testing for predictability in a noninvertible ARMA model," MPRA Paper 37151, University Library of Munich, Germany.
    2. Lanne Markku & Saikkonen Pentti, 2011. "Noncausal Autoregressions for Economic Time Series," Journal of Time Series Econometrics, De Gruyter, vol. 3(3), pages 1-32, October.
    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.

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