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Minimum Contrast Estimation for Fractional Diffusions

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  • Carenne Ludeña

Abstract

. 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 Xt 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.

Suggested Citation

  • Carenne Ludeña, 2004. "Minimum Contrast Estimation for Fractional Diffusions," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 31(4), pages 613-628, December.
    • Handle: RePEc:bla:scjsta:v:31:y:2004:i:4:p:613-628
    DOI: 10.1111/j.1467-9469.2004.00410.x
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