LAN property for some fractional type Brownian motion

Abstract

International audienceWe 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_\theta\PAR{x} \sim_{x\to 0} \ABS{x}^{-\al(\theta)}L_\theta(x) with $L_\theta$ a slowly varying function and \al\PAR{\theta}\in (-\infty,1). We prove LAN property for these models which include in particular fractional Brownian motion %$B^\alpha_t,\: \alpha \geq 1/2$ or ARFIMA processes