Worth noting is the misleading aspect that level changes in the index value in '88 are higher than in later years due to the nature of returns as percentage changes.
A dumb way to do this would be to write some code that identifies returns that are larger than its past and future immediate neighbors. That would tell you the average gap between local maxima is 2 weeks with standard deviation of 0.16. But you're not dumb, so you didn't do that.
Another way could be to find the gap between positive returns that lie outside a deviation, but gradual peaks dodge that method.
I'm not doing this to be academic and thorough, so I'm going to think practically about it. To Paint!
Looking at this, it's recognizable pretty quickly that I'm mistaking a lack of stagnancy for periodicity. Saying that the index fluctuates isn't the same thing as saying the index fluctuates with a pattern.
If I'm going to waste my time testing for something as bold as periodicity, I'm not going to do it on index returns from 20 years ago when even the second run of the eyeball test fails.
And if you wasted your time reading this, what does that say about you?
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