LAN property for some fractional type Brownian motion

Abstract

We study asymptotic expansion of the likelihood of a certain class of Gaussian processes characterized by their spectral density $f_{\theta }$. We consider the case where $f_θ\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(θ)}L_θ(x)$ with $L_{\theta }$ a slowly varying function and $\al\PARθ\in (-\infty,1)$. We prove LAN property for these models which include in particular fractional Brownian motion %$B_t^{\alpha },\alpha \ge 1/2$ or ARFIMA processes.

References in corpus (1)

• Correction. Efficient parameter estimation for self-similar processes