Thiele Seminar: Mark Podolskij, Aarhus University and CREATES

Title: Estimation of the Linear Fractional Motion

Info about event


Thursday 7 September 2017,  at 13:15 - 14:00


Department of Mathematics, Ny Munkegade 118, room Koll. G (1532-214)


In this talk we investigate the parametric inference for the linear fractional stable motion in the high frequency setting. The symmetric linear fractional stable motion is a three-parameter family, which constitutes a natural non-Gaussian analogue of the scaled fractional Brownian motion. It is fully characterised by the scaling parameter ?>0, the self-similarity parameter H?(0,1) and the stability index ??(0,2) of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments Lévy moving average processes that has been recently established. More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of (?,?,H). We present the law of large numbers and some fully feasible weak limit theorems.

Joint work with Stepan Mazur and Dmitry Otryakhin.