Levy distributions keep identical form across every timescale, making scale irrelevant

Evidence

Levy distributions have the elegant property that we now call “selfsimilarity.” Price changes in longer time periods are simply the sum of changes in shorter time periods, and Levy distributions are invariant under addition. If changes in short time periods were independent and all followed the same Levy distribution, then so would changes over longer periods. The “scale” used in the analysis time periods of a minute, an hour, a day, a week, a month, a year would therefore not matter: the form of the distribution would be unchanged. — Donald MacKenzie, An Engine, Not a Camera, 492

Categorization

• DEFINE: Selfsimilarity — the scale-invariance property — is defined concretely here.
• XREF: connects to: Under a Gaussian distribution extreme tail events become effectively impossible — Mark Blyth, Austerity: The History of a Dangerous…, 106; Empirical aggregation tests undercut the Levy distribution’s self-similarity claim — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 507; Levy distributions yield more stable estimates of extreme moves than variance-based methods — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 937 (+1 more)

Broader Connections

• Empirical aggregation tests undercut the Levy distribution’s self-similarity claim #contradicts (0.90) — Donald MacKenzie, An Engine, Not a Camera, 507
• The Levy distribution’s failure to survive time aggregation cooled academic interest in fat tails #qualifies (0.85) — Donald MacKenzie, An Engine, Not a Camera, 509
• Levy distributions yield more stable estimates of extreme moves than variance-based methods #expands (0.70) — Donald MacKenzie, An Engine, Not a Camera, 937