Probability density function (pdf) of the time of occurrence of grand minima (panel A)) and grand maxima (panel B)) relative to the time of occurrence of the nearest low and high, respectively, of the Hallstatt cycle, using the superposed epoch analysis. The times of occurrence of highs and lows of the Hallstatt cycle are defined by considering the average of the two curves (second SSA components of the SN-14C and SN-10Be series) shown in Fig. 3C (leading to 5530 BC, 3650 BC, 810 BC, and 1510 AD for the lows and to 6670 BC, 4600 BC, 1970 BC, and 160 AD for the highs).