Expectiles for subordinated Gaussian processes with applications

Abstract

International audienceIn this paper, we introduce a new class of estimators of the Hurst exponent of the fractional Brownian motion (fBm) process. These estimators are based on sample expectiles of discrete variations of a sample path of the fBm process. In order to derive the statistical properties of the proposed estimators, we establish asymptotic results for sample expectiles of subordinated stationary Gaussian processes with unit variance and correlation function satisfying $\rho(i)\sim \kappa|i|^{-\alpha}$ ($\kappa\in \RR$) with $\alpha>0$. Via a simulation study, we demonstrate the relevance of the expectile-based estimation method and show that the suggested estimators are more robust to data rounding than their sample quantile-based counterparts

Statistical test for fractional Brownian motion based on detrending moving average algorithm

“…However, most of the works mainly concern various methods of estimating the parameters of the FBM model. They are based, among others, on p-variation [45], discrete variation [19], sample quantiles [20] and other methods [9,12,21,27,43,52,74,81]. A certain gap in this theory is the lack of tools such as rigorous statistical tests to identify the FBM model in empirical data.…”