Scandinavian Working Papers in Economics

# No 2018:3: Estimation of the linear fractional stable motion

Stepan Mazur (), Dmitry Otryakhin () and Mark Podolskij ()
Stepan Mazur: Örebro University School of Business, Postal: Örebro University, School of Business, SE - 701 82 ÖREBRO, Sweden
Dmitry Otryakhin: Aarhus University, Postal: Ny Munkegade 118, 8000 Aarhus C, Denmark
Mark Podolskij: Aarhus University, Postal: Ny Munkegade 118, building 1535, 317, 8000 Aarhus C, Denmark

Abstract: In this paper we investigate the parametric inference for the linear fractional stable motion in high and low 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 $\sigma>0$, the self-similarity parameter $H \in (0,1)$ and the stability index $\alpha \in (0,2)$ of the driving stable motion. The parametric estimation of the model is inspired by the limit theory for stationary increments L\'evy moving average processes that has been recently studied in \cite{BLP}. More specifically, we combine (negative) power variation statistics and empirical characteristic functions to obtain consistent estimates of $(\sigma, \alpha, H)$. We present the law of large numbers and some fully feasible weak limit theorems.

JEL-codes: C00; C13

38 pages, February 20, 2018

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