Identification of the Multivariate Fractional Brownian Motion

Abstract

This paper deals with the identification of the multivariate fractional Brownian motion, a recently developed extension of the fractional Brownian motion to the multivariate case. This process is a $p$-multivariate self-similar Gaussian process parameterized by $p$ different Hurst exponents $H_i$, $p$ scaling coefficients ${\sigma }_i$ (of each component) and also by $p(p-1)$ coefficients ${\rho }_{ij},{\eta }_{ij}$ (for $i,j=1,...,p$ with $j>i$) allowing two components to be more or less strongly correlated and allowing the process to be time reversible or not. We investigate the use of discrete filtering techniques to estimate jointly or separately the different parameters and prove the efficiency of the methodology with a simulation study and the derivation of asymptotic results.

References in corpus (5)

• Integral representations and properties of operator fractional Brownian motions
• Cross-correlation of long-range correlated series
• Covariance function of vector self-similar process
• Basic properties of the Multivariate Fractional Brownian Motion
• Multiple local whittle estimation in stationary systems

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• Wavelet analysis of the multivariate fractional Brownian motion
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• Non-Linear Wavelet Regression and Branch & Bound Optimization for the Full Identification of Bivariate Operator Fractional Brownian Motion
• Multifractal temporally weighted detrended partial cross-correlation analysis to quantify intrinsic power-law cross-correlation of two non-stationary time series affected by common external factors
• Two-dimensional Brownian motion with dependent components: turning angle analysis
• Tangent fields, intrinsic stationarity, and self-similarity (with a supplement on Matheron Theory)