The Davenport spectrum is a modification of the classical Kolmogorov spectrum for the inertial range of turbulence that accounts for non-scaling low frequency behavior. Like the classical fractional Brownian motion vis-à-vis the Kolmogorov spectrum, tempered fractional Brownian motion (tfBm) is a new model that displays the Davenport spectrum. The autocorrelation of the increments of tfBm displays semi-long range dependence (hyperbolic and quasi-exponential decays over moderate and large scales, respectively), a phenomenon that has been observed in a wide range of applications from wind speeds to geophysics to finance. In this paper, we use wavelets to construct the first estimation method for tfBm and a simple and computationally efficient test for fBm vs tfBm alternatives. The properties of the wavelet estimator and test are mathematically and computationally established. An application of the methodology shows that tfBm is a better model than fBm for a geophysical flow data set.

Davenport频谱是经典Kolmogorov频谱的修正形式，用于湍流的惯性范围，这说明了非标度低频行为。像相对于Kolmogorov谱图的经典分数布朗运动一样，回火分数布朗运动（tfBm）是显示Davenport谱的新模型。tfBm增量的自相关显示了半长距离依赖性（分别在中等和较大尺度上发生了双曲线和准指数衰减），这种现象已在从风速到地球物理到金融的广泛应用中被观察到。在本文中，我们使用小波构造了tfBm的第一种估计方法，并针对fBm与tfBm替代方案建立了一种简单且计算效率高的测试。在数学和计算上建立了小波估计器和测试的属性。该方法的应用表明，对于地球物理流量数据集，tfBm比fBm更好。