Statistical significance testing for the association of magnetometer records at high-, mid- and low latitudes during substorm days

In recent years, the interaction of the auroral substorms with the equatorial and mid-latitude currents has been the subject of extensive research. We introduce a new statistical technique that allows us to test at a specified significance level whether such a dependence exists, and how long it persists. This quantitative statistical technique, relying on the concepts and tools of functional data analysis, uses directly magnetometer records in one minute resolution, and it can be applied to similar geophysical data which can be represented as daily curves. It is conceptually similar to testing the nullity of the slope in the straight line regression, but both the regressors and the responses are curves rather than points. When the regressors are daily high latitude H-component curves during substorm days and the responses are daily mid- or low latitude H-component curves, our test shows significant dependence (the nullity hypothesis is rejected) which exists not only on the same UT day but also extends into the next day for strong substorms.