How to estimate the memory of the Elephant Random Walk
Language
en
Article de revue
This item was published in
Communications in Statistics - Theory and Methods. 2022-11-01p. 1-21
Taylor & Francis
English Abstract
We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more ...Read more >
We introduce an original way to estimate the memory parameter of the elephant random walk, a fascinating discrete time random walk on integers having a complete memory of its entire history. Our estimator is nothing more than a quasi-maximum likelihood estimator, based on a second order Taylor approximation of the log-likelihood function. We show the almost sure convergence of our estimate in the diffusive, critical and superdiffusive regimes. The local asymptotic normality of our statistical procedure is established in the diffusive regime, while the local asymptotic mixed normality is proven in the superdiffusive regime. Asymptotic and exact confidence intervals as well as statistical tests are also provided. All our analysis relies on asymptotic results for martingales and the quadratic variations associated.Read less <
English Keywords
Elephant random walk
Maximum likelihood estimation
Almost sure convergence
Local asymptotic normality
Origin
Hal imported