> Far from it, What? While I'm reading your references, let's be clear on what you are saying: On the one hand, in the context of the OP, we're talking about

> Far from it, What? While I'm reading your references, let's be clear on what you are saying: On the one hand, in the context of the OP, we're talking about flairs, as essentially discrete events, 'points' in a 'point process', over time intervals from the present back to at least 1889 or whenever it was, that is, over 100 years, and, if we could get more data, thousands or millions of years and (2) what happens in detail with the sun spots, the 11 year sun spot cycle, the magnetic field of the sun, etc. So, sure, on short time scales, say, within one 'point' there can be a lot of dependence, that is, lack of 'independent increments'. But for these 'points' over years, centuries, or millennia? You are saying that there is a dependence between a flair today and 11 years from now? Assuming that the 'dangerous flairs' are more common when sun spots are in the 11 year cycle, for modeling the stochastic arrival process over several decades, centuries, etc. we should, first-cut, and I saw a lot of first-cutting when I was in physics class, 'smooth out' the 11 year cycle and continue on. Then, tough to believe that you are claiming dependence between points separated by months or years. E.g., I see in your [2] in Figure 2 on page 463 a distribution of waiting times with the horizontal axis a log scale up to 10,000 hours but clearly nearly all the probability mass less than 100 hours, here being sure to note the log scale on the vertical axis. So, in the context of the OP, that 100 hours is within just one particular 'point' in the stochastic point process and essentially irrelevant when considering years, decades, centuries, etc. So, the independent increments assumption seems to continue to hold. And with the smearing out, so does the stationarity. Then, from Cinlar, presto, a Poisson process. Oops: Apparently the Maunder minimum, as in the graph below in this thread, kills off the stationarity assumption, even with the 'smoothing'. So, apparently until we can understand things like the Maunder minimum, we're really short on a good stochastic point process model of sun spots and maybe also dangerous CMEs. Then maybe the best we have is just observe that both humans and life on earth have been around a long time and in some intuitive sense the sun seems fairly 'stable' in some meaningful sense so that we can guess we will still be here a long time. Math fails again!