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Minimum Contrast Estimation for Fractional Diffusions
Author(s) -
Ludeña Carenne
Publication year - 2004
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2004.00410.x
Subject(s) - mathematics , estimator , fractional brownian motion , context (archaeology) , contrast (vision) , hurst exponent , mathematical analysis , brownian motion , limit (mathematics) , statistics , paleontology , artificial intelligence , computer science , biology
. When the Hurst coefficient of a fractional Brownian motion is greater than 1/2 it is possible to define a stochastic integral with respect to , as the pathwise limit of Riemann sums, and thus to consider pathwise solutions to fractional diffusion equations. In this paper, we consider the vanishing drift case and assume that the solution X t is parameterized by θ in a compact parameter space Θ . Our main interest is the estimation of θ based on discrete time, but with very frequent observations. It is shown that the estimation problem in this context is locally asymptotically mixed normal. The asymptotic behaviour of a certain class of minimum contrast estimators is then studied and asymptotic efficiency is discussed.