Selection of sparse multifractional model

Pierre, Raphael Bertrand (1) , Marie-Eliette Dury (2, 1) , Nabiha Haouas (3, 1)

1 PAS
2 UdA - Université d'Auvergne - Clermont-Ferrand I
3 Université de Sousse

The aim of this paper is to provide a simple model with a time-varying Hurst index. Such models should be both the simplest possible and fit well the real Hurst index. Moreover this would avoid a numerical artefact pointed out in this article. For this, after a recall on fBm, mBm and statistical estimation of the Hurst index, including a time-varying one, we propose a fitting test for a model with a time-varying Hurst index. Then an approach is given to select the most simple model.

Mots clés: fractional Brownian motion (fBm); multifractional Brownian motion (mBm); Hurst index; Model selection; Sparse model; Big data; Portemanteau test; Quantitative finance; Efficient Market Hypothesis; Behavioural finance

Domaines: Applications [stat.AP]; Méthodologie [stat.ME]; Théorie [stat.TH]

Pierre, Raphael Bertrand, Marie-Eliette Dury, Nabiha Haouas. Selection of sparse multifractional model. 2015. ⟨hal-01194347⟩