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Tempered fractional Brownian motion (TFBM) modifies the power law kernel in the moving average representation of a fractional Brownian motion, adding an exponential tempering. Tempered fractional Gaussian noise (TFGN), the increments of TFBM, form a stationary time series that can exhibit semi-long range dependence. This paper develops the basic theory of TFBM, including moving average and spectral...
A new approach to extreme value theory is presented for vector data with heavy tails. The tail index is allowed to vary with direction, where the directions are not necessarily along the coordinate axes. Basic asymptotic theory is developed, using operator regular variation and extremal integrals. A test is proposed to judge whether the tail index varies with direction in any given data set.
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