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<p>In order to examine the behavior of the quasi-maximum likelihood function in the context of GARCH processes, we study the Kalman filter for this model in its state-space form and derive the necessary assumptions on the parameter space under which asymptotic stability holds. In particular, we prove that the quasi-maximum likelihood estimator is consistent.</p>

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The Strong Consistency of Quasi-Maximum Likelihood Estimator for GARCH Models

  • 期刊论文

  • 发表日期：

    2026年5月5日

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  • Mohammed Benmoumen,
  • Imane Salhi

摘要

In order to examine the behavior of the quasi-maximum likelihood function in the context of GARCH processes, we study the Kalman filter for this model in its state-space form and derive the necessary assumptions on the parameter space under which asymptotic stability holds. In particular, we prove that the quasi-maximum likelihood estimator is consistent.