Cumulative areawise testing in wavelet analysis and its application to geophysical time series

Abstract

Statistical significance testing in wavelet analysis was improved through the development of a cumulative areawise test. The test was developed to eliminate the selection of two significance levels that an existing geometric test requires for implementation. The selection of two significance levels was found to make the test sensitive to the chosen pointwise significance level, which may preclude further scientific investigation. A set of experiments determined that the cumulative areawise test has greater statistical power than the geometric test in most cases, especially when the signal-to-noise ratio is high. The number of false positives identified by the tests was found to be similar if the respective significance levels were set to 0.05.