In one of Mandelbrot's original works on "scale invariance," he studied the cotton markets around the mid- to late 19th century and found that the shape of the price versus time graphs were similar no matter whether you measured the average price per week or month. A discovery of any kind of invariance is an important fact about how the way the world works. No matter how quirky the invariance is, any theory worth being called a theory needs to explain the invariance's existence.
The above graph is not scale invariant. But it might be multi-scale invariant. Much depends on what will happen in the next week or so.
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