Do statistically significant correlations exist between the homestake solar neutrino data and sunspots?

It has been suggested by various authors that a significant anticorrelation exists between the Home-stake solar neutrino data and the sunspot cycle. Some of these claims rest on smoothing the data by taking running averages, a method that has recently undergone criticism. We demonstrate that no significant anticorrelation can be found in the Homestake data, or in standard averages of that data. However, when running averages are taken, an anticorrelation seems to emerge whose significance grows as the number of points in the average increases. Our analysis indicates that the apparently high significance of these anticorrelations is an artifact of the failure to consider the loss of independence introduced in the running average process. When this is considered, the significance is reduced to that of the unaveraged data. Furthermore, when evaluated via parametric subsampling, no statistically significant anticorrelation is found. We conclude that the Homestake data cannot be used to substantiate any claim of an anticorrelation with the sunspot cycle.