2018/08/14 by B. Cooper Boniece, Boniece, B. Cooper, Gustavo Didier +3
Economics, Econometrics and Finance · Mathematics · #42C40 #60G18 #62M10 #Complex Systems and Time Series Analysis #FOS: Mathematics #Financial Risk and Volatility Modeling #Probability (math.PR) #Statistical and numerical algorithms #Statistics Theory (math.ST)
paper · pdf · doi:10.48550/arxiv.1808.04935
openalex publication_date 2018/08/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The Davenport spectrum is a modification of the classical Kolmogorov spectrum\nfor the inertial range of turbulence that accounts for non-scaling low\nfrequency behavior. Like the classical fractional Brownian motion vis- `a-vis\nthe Kolmogorov spectrum, tempered fractional Brownian motion (tfBm) is a\ncanonical model that displays the Davenport spectrum. The autocorrelation of\nthe increments of tfBm displays semi-long range dependence (hyperbolic and\nquasi-exponential decays over moderate and large scales, respectively), a\nphenomenon that has been observed in wide a range of applications from wind\nspeeds to geophysics to finance. In this paper, we use wavelets to construct\nthe first estimation method for tfBm and a simple and computationally efficient\ntest for fBm vs tfBm alternatives. The properties of the wavelet estimator and\ntest are mathematically and computationally established. An application of the\nmethodology to the analysis of geophysical flow data shows that tfBm provides a\nmuch closer fit than fBm.\n