Empirical aggregation tests undercut the Levy distribution’s self-similarity claim

Evidence

One trigger of the loss of support was the work of the University of Chicago Ph.D. student Robert R. Officer, who applied Fama and Roll’s improved methods of estimating alpha and found that its value rose as daily stock-price data were aggregated into longer time periods, behavior that was at odds with self-similarity or invariance under addition (Officer 1972). — Donald MacKenzie, An Engine, Not a Camera, 507

Categorization

• XREF: The self-similarity/invariance-under-addition property connects to scale-invariance debates in fractal geometry and Mandelbrot’s broader program. — connects to: A single exponent alpha parametrizes a family spanning normal to wildly fatal-tailed distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 479; Levy distributions keep identical form across every timescale, making scale irrelevant — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 492; A finite sample’s variance cannot distinguish a fat-tailed from an infinite-variance distribution — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 499 (+6 more)

Broader Connections

• The Levy distribution’s failure to survive time aggregation cooled academic interest in fat tails #corroborates (0.90) — Donald MacKenzie, An Engine, Not a Camera, 509
• Levy distributions yield more stable estimates of extreme moves than variance-based methods #complicates (0.78) — Donald MacKenzie, An Engine, Not a Camera, 937
• Deliberately assuming wild randomness can paradoxically keep markets mild #complicates (0.75) — Donald MacKenzie, An Engine, Not a Camera, 1169