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Activity Number: 403 - SPAAC Poster Competition
Type: Topic Contributed
Date/Time: Tuesday, July 30, 2019 : 2:00 PM to 3:50 PM
Sponsor: Section on Statistics and the Environment
Abstract #300654
Title: Wavelet Variances for Heavy-Tailed Time Series
Author(s): Rodney Fonseca* and Debashis Mondal and Lingjiao Zhang
Companies: University of Campinas and Oregon State University and University of Pennsylvania
Keywords: Characteristic scale; Daubechies wavelet; Discrete wavelet transform; Hill estimator; Stable asymptotics; Tail index

This work focuses on wavelet analysis of variability for heavy-tailed time series. Under the assumption that time series values have finite second but infinite fourth moments, stable asymptotics are derived for wavelet variances across different time scales. These stable asymptotics have a slower rate of convergence than the square root of the sample size and are markedly different from conventional normal asymptotics. Furthermore, the asymptotic results apply even when the time series exhibit a long range dependence. Wavelet variances and stable asympotics are then used to analyze three streamflows; one in Arizona, one in Connecticut and the other in Illinois. These analyses provide a deeper understanding of streamflow variability at different time scales (e.g., extreme variation at short time scales that are characteristic of heavy rainfall, presence of seasonal variations, and, in one case, some quasi-biennial fluctuations). Furthermore, this work includes evaluations of local characteristic time scales, a discussion of tail heaviness, computation of Hurst exponents, and some future directions of research.

Authors who are presenting talks have a * after their name.

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