Would it be possible for you to share any of the code you used to obtain these results? This post has inspired me to run some follow-up analyses of my own along similar lines, and having access to this code as a starting point would make that somewhat easier.
More structure emerges! Here's a plot of consecutive pairs of values (data[i], data[i+1]) such that data[i+1] = -data[i+2]. 
Would it be possible for you to share any of the code you used to obtain these results? This post has inspired me to run some follow-up analyses of my own along similar lines, and having access to this code as a starting point would make that somewhat easier.