Trends from Levy-walk statistics in solar activity - a link to multidecadal and secular trends in Earth climate?

We present a critique of an hypothesis advocating the view that there exists a ”complexity linkage” between solar activity and Earth climate which explains a major part of the trend in in Earth global temperature over the last century. This hypothesis contends that the waiting times between hard X-ray solar flares obey Levy-walk statistics governed by one characteristic exponent, and that this statistics with the same exponent can be discerned in other solar time series like the sunspot number and total irradiance, and even in the Earth global temperature. A consequence of this hypothesis is that Levy-walk statistics will give rise to slow trends in the signal representing the frequency of hard flares, and that the underlying characteristic exponent can be uniquely retrieved from the trend signal. We demonstrate that there is no Levy-walk statistics for solar flares on time scales longer than 3 months, that the characteristic exponent for sunspot numbers and solar irradiance is drastically changed when the periodic trend of the solar cycle is eliminated, and that it is impossible to retrieve this exponent from the trends in the sunspot record or the 150 year long instrumental global temperature record. Thus, the hypothesis that this trend is a result of an underlying Levy-walk statistic is impossible to falsify by analysis of existing observational data.