A novel matrix-valued Hurst operator construction for 2D fBm with cross-dependencies is introduced, with derived auto/cross-covariances and power spectral densities validated by simulations.
Basic properties of the Multivariate Fractional Brownian Motion
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abstract
This paper reviews and extends some recent results on the multivariate fractional Brownian motion (mfBm) and its increment process. A characterization of the mfBm through its covariance function is obtained. Similarly, the correlation and spectral analyses of the increments are investigated. On the other hand we show that (almost) all mfBm's may be reached as the limit of partial sums of (super)linear processes. Finally, an algorithm to perfectly simulate the mfBm is presented and illustrated by some simulations.
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UNVERDICTED 2representative citing papers
Extends rough fractional stochastic volatility to a multivariate fOU model with GMM estimation, simulation validation, and empirical analysis of realized volatility series showing correlations and spillover effects.
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Two-dimensional fractional Brownian motion: Analysis in time and frequency domains
A novel matrix-valued Hurst operator construction for 2D fBm with cross-dependencies is introduced, with derived auto/cross-covariances and power spectral densities validated by simulations.
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Multivariate Rough Volatility
Extends rough fractional stochastic volatility to a multivariate fOU model with GMM estimation, simulation validation, and empirical analysis of realized volatility series showing correlations and spillover effects.