Articles | Volume 26, issue 2
Research article
14 Jun 2019
Research article |  | 14 Jun 2019

Statistical hypothesis testing in wavelet analysis: theoretical developments and applications to Indian rainfall

Justin A. Schulte

Related authors

A skewed perspective of the Indian rainfall–El Niño–Southern Oscillation (ENSO) relationship
Justin Schulte, Frederick Policielli, and Benjamin Zaitchik
Hydrol. Earth Syst. Sci., 24, 5473–5489,,, 2020
Short summary
Long Island Sound temperature variability and its associations with the ridge–trough dipole and tropical modes of sea surface temperature variability
Justin A. Schulte and Sukyoung Lee
Ocean Sci., 15, 161–178,,, 2019
Short summary
Wavelet analysis for non-stationary, nonlinear time series
Justin A. Schulte
Nonlin. Processes Geophys., 23, 257–267,,, 2016
Cumulative areawise testing in wavelet analysis and its application to geophysical time series
Justin A. Schulte
Nonlin. Processes Geophys., 23, 45–57,,, 2016
Short summary
Geometric and topological approaches to significance testing in wavelet analysis
J. A. Schulte, C. Duffy, and R. G. Najjar
Nonlin. Processes Geophys., 22, 139–156,,, 2015

Related subject area

Subject: Time series, machine learning, networks, stochastic processes, extreme events | Topic: Climate, atmosphere, ocean, hydrology, cryosphere, biosphere
Rain process models and convergence to point processes
Scott Hottovy and Samuel N. Stechmann
Nonlin. Processes Geophys., 30, 85–100,,, 2023
Short summary
Integrated hydrodynamic and machine learning models for compound flooding prediction in a data-scarce estuarine delta
Joko Sampurno, Valentin Vallaeys, Randy Ardianto, and Emmanuel Hanert
Nonlin. Processes Geophys., 29, 301–315,,, 2022
Short summary
Empirical adaptive wavelet decomposition (EAWD): an adaptive decomposition for the variability analysis of observation time series in atmospheric science
Olivier Delage, Thierry Portafaix, Hassan Bencherif, Alain Bourdier, and Emma Lagracie
Nonlin. Processes Geophys., 29, 265–277,,, 2022
Short summary
Predicting sea surface temperatures with coupled reservoir computers
Benjamin Walleshauser and Erik Bollt
Nonlin. Processes Geophys., 29, 255–264,,, 2022
Short summary
Lévy noise versus Gaussian-noise-induced transitions in the Ghil–Sellers energy balance model
Valerio Lucarini, Larissa Serdukova, and Georgios Margazoglou
Nonlin. Processes Geophys., 29, 183–205,,, 2022
Short summary

Cited articles

Adarsh, S. and Reddy M. J.: Trend analysis of rainfall in four meteorological subdivisions of southern India using nonparametric methods and discrete wavelet analysis, Int. J. Climatol., 35, 1107–1124, 2014. 
Addison, P. S.: Wavelet transforms and the ECG: a review, Physiol. Meas., 26, R155,, 2005. 
Agarwal, A., Maheswaran, R., Marwan, N., Caesar, L., and Kurths, J.: Wavelet-based multiscale similarity measure for complex networks, Eur. Phys. J. B, 91, 296,, 2018. 
Azad, S., Vignesh, T. S., and Narasimha, R.: Periodicities in Indian Monsoon Rainfall over spectrally homogeneous regions, Int. J. Climatol., 30, 2289–2298, 2010. 
Edelsbrunner, H. and Harer, J.: Persistent homology-a survey, Contemp. Math., 453, 257–282, 2008. 
Short summary
Statistical hypothesis tests in wavelet analysis are used to asses the likelihood that time series features are noise. The choice of test will determine which features emerge as a signal. Tests based on area do poorly at distinguishing abrupt fluctuations from periodic behavior, unlike tests based on arclength that do better. The application of the tests suggests that there are features in Indian rainfall time series that emerge from background noise.