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The Davenport spectrum is a modification of the classical Kolmogorov spectrumfor the inertial range of turbulence that accounts for non-scaling lowfrequency behavior. Like the classical fractional Brownian motion vis-\`a-visthe Kolmogorov spectrum, tempered fractional Brownian motion (tfBm) is acanonical model that displays the Davenport spectrum. The autocorrelation ofthe increments of tfBm displays semi-long range dependence (hyperbolic andquasi-exponential decays over moderate and large scales, respectively), aphenomenon that has been observed in wide a range of applications from windspeeds to geophysics to finance. In this paper, we use wavelets to constructthe first estimation method for tfBm and a simple and computationally efficienttest for fBm vs tfBm alternatives. The properties of the wavelet estimator andtest are mathematically and computationally established. An application of themethodology to the analysis of geophysical flow data shows that tfBm provides amuch closer fit than fBm.

Tempered fractional Brownian motion: wavelet estimation, modeling and testing