Abstract
We consider a stable autoregressive model of order p. We establish, for the gradient estimator, a central limit theorem, a law of the iterated logarithm and an almost sure central limit theorem; a quadratic strong law of large numbers is proved for the estimation and for the associated prediction. Then we give a new estimator, the averaged gradient estimator, which is computed more easily than the classical least squares estimator, and enjoys the same optimal asymptotic properties as the latter.
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More From: Comptes Rendus de l'Academie des Sciences Series I Mathematics
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