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Nonlinear Processes in Geophysics An interactive open-access journal of the European Geosciences Union
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Discussion papers
https://doi.org/10.5194/npg-2018-55
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.
https://doi.org/10.5194/npg-2018-55
© Author(s) 2018. This work is distributed under
the Creative Commons Attribution 4.0 License.

Research article 13 Dec 2018

Research article | 13 Dec 2018

Review status
This discussion paper is a preprint. It is a manuscript under review for the journal Nonlinear Processes in Geophysics (NPG).

Statistical Hypothesis Testing in Wavelet Analysis: Theoretical Developments and Applications to India Rainfall

Justin A. Schulte Justin A. Schulte
  • Science Systems and Applications, Inc, Lanham, 20782, United States

Abstract. Statistical hypothesis tests in wavelet analysis are reviewed and developed. The output of a recently developed cumulative area-wise is shown to be the ensemble mean of individual estimates of statistical significance calculated from a geometric test assessing statistical significance based on the area of contiguous regions (i.e. patches) of point-wise significance. This new interpretation is then used to construct a simplified version of the cumulative area-wise test to improve computational efficiency. Ideal examples are used to show that the geometric and cumulative area-wise tests are unable to differentiate features arising from singularity-like structures from those associated with periodicities. A cumulative arc-wise test is therefore developed to test for periodicities in a strict sense. A previously proposed topological significance test is formalized using persistent homology profiles (PHPs) measuring the number of patches and holes corresponding to the set of all point-wise significance values. Ideal examples show that the PHPs can be used to distinguish time series containing signal components from those that are purely noise. To demonstrate the practical uses of the existing and newly developed statistical methodologies, a first comprehensive wavelet analysis of India rainfall is also provided. A R-software package has been written by the author to implement the various testing procedures.

Justin A. Schulte
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Status: final response (author comments only)
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Justin A. Schulte
Justin A. Schulte
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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 what features emerge as a signal. Tests based on area do poorly at distinguishing abrupt fluctuations from periodic behavior unlike tests based on arc length that do better. The application of the tests suggests that there are features in India rainfall time series that emerge from background noise.
Statistical hypothesis tests in wavelet analysis are used to asses the likelihood that time...
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