Modelling NASDAQ Series by Sparse Multifractional Brownian Motion

被引：15

作者：

Bertrand, Pierre R. ^{[1
,2
]}

Hamdouni, Abdelkader ^{[3
]}

Khadhraoui, Samia ^{[4
]}

机构：

[1] INRIA Saclay, Lab Math UMR CNRS, F-6620 Aubiere, France

[2] Clermont Univ, F-6620 Aubiere, France

[3] Univ Monastir, Fac Sci, Computat Math Lab, Monastir 5019, Tunisia

[4] Inst Super Gest, Sousse 4000, Tunisia

来源：

METHODOLOGY AND COMPUTING IN APPLIED PROBABILITY | 2012年 / 14卷 / 01期

关键词：

Model selection; Finance; Fractional Brownian motion; Multi-fractional Brownian motion; Generalized quadratic variation; Wavelet analysis; WAVELET ANALYSIS; LOCAL-STRUCTURE; ARBITRAGE; IDENTIFICATION; VERSION;

D O I：

10.1007/s11009-010-9188-5

中图分类号：

O21 [概率论与数理统计]; C8 [统计学];

学科分类号：

020208 ; 070103 ; 0714 ;

摘要：

The objective of this paper is to compare the performance of different estimators of Hurst index for multifractional Brownian motion (mBm), namely, Generalized Quadratic Variation (GQV) Estimator, Wavelet Estimator and Linear Regression GQV Estimator. Both estimators are used in the real financial dataset Nasdaq time series from 1971 to the 3rd quarter of 2009. Firstly, we review definitions, properties and statistical studies of fractional Brownian motion (fBm) and mBm. Secondly, a numerical artifact is observed: when we estimate the time varying Hurst index H(t) for an mBm, sampling fluctuation gives the impression that H(t) is itself a stochastic process, even when H(t) is constant. To avoid this artifact, we introduce sparse modelling for mBm and apply it to Nasdaq time series.

引用

页码：107 / 124

页数：18

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