Figure 4. Results of a long simulation of 183 large “earthquakes”. We have constructed a time series \(\Theta_{\text{sim}}(t)\) using equation (4), which yields results generally similar to those in Figures 1 and 3. a) Time series \(\Theta_{\text{sim}}(t)\) as a function of ”time” in ”months” on the left, PPV on the right. Compare to Figure 3. The vertical red line at bottom of the time series is the large ”earthquake”, the dashed blue line is the derivative of the time series representing the activity. On the left is the time series, on the right is the associated Precision (PPV). b) ROC curve for the time series as discussed in the text. Area of 0.88 under the ROC curve is larger than 0.5, indicating skill. Cyan curves are the skill from 50 random time series. c) Histogram of intervals between 183 large ”earthquakes”. d) Cumulative interval statistics, obtained from integrating histogram in c). Also shown is the dashed curve for Poisson (exponential) statistics having the same mean as the time series.