Maximum likelihood estimators and random walks in long memory models

2007/11/04 by Karine Bertin, Bertin, Karine, Soledad Torres +3
Mathematics · #FOS: Mathematics #Probability (math.PR) #Statistics Theory (math.ST) #math.PR #math.ST #stat.TH

paper · pdf · doi:10.48550/arxiv.0711.0513

To appear in "Statistics"

arxiv created 2009/12/19 · arxiv updated 2010/01/07

Abstract

We consider statistical models driven by Gaussian and non-Gaussian self-similar processes with long memory and we construct maximum likelihood estimators (MLE) for the drift parameter. Our approach is based on the approximation by random walks of the driving noise. We study the asymptotic behavior of the estimators and we give some numerical simulations to illustrate our results.

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