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Asymptotic behavior of M-estimators in AR(p) models under nonstandard conditions

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  • Marc Hallin
  • Faouzi El Bantli

Abstract

The authors derive the limiting distribution of M-estimators in AR(p) models under nonstandard conditions, allowing for discontinuities in score and density functions. Unlike usual regularity assumptions, these conditions are satisfied in the context of L1-estimation and autoregression quantiles. The asymptotic distributions of the resulting estimators, however, are not generally Gaussian. Moreover, their bootstrap approximations are consistent along very specific sequences of bootstrap sample sizes only.

Suggested Citation

  • Marc Hallin & Faouzi El Bantli, 2001. "Asymptotic behavior of M-estimators in AR(p) models under nonstandard conditions," ULB Institutional Repository 2013/2105, ULB -- Universite Libre de Bruxelles.
  • Handle: RePEc:ulb:ulbeco:2013/2105
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    Cited by:

    1. Duchesne, Pierre, 2004. "On robust testing for conditional heteroscedasticity in time series models," Computational Statistics & Data Analysis, Elsevier, vol. 46(2), pages 227-256, June.

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