A finite sample’s variance cannot distinguish a fat-tailed from an infinite-variance distribution

Evidence

Fama concluded that the distributions of stock-price changes were unequivocally fat-tailed. Were they Levy distributions? Were their variances infinite? Those were harder questions to answer. In any sample of finite size, the sample variance will always be finite even if the underlying distribution has an infinite variance, so these questions cannot be answered by calculating a variance. — Donald MacKenzie, An Engine, Not a Camera, 499

Categorization

• XREF: connects to: Contradictory econometric results cannot be adjudicated a priori — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 108; Below alpha of 2, distributions have no finite variance at all — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 480; A single exponent alpha parametrizes a family spanning normal to wildly fatal-tailed distributions — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 479 (+6 more)

Broader Connections

• Large samples produce significant correlations that explain little variance #expands (0.80) — Roderick M. Kramer, Geoffrey J. Leonardelli, Robert W. Livingston, Social Cognition, Social Identity, and…, 1036
• Empirical aggregation tests undercut the Levy distribution’s self-similarity claim #contradicts (0.78) — Donald MacKenzie, An Engine, Not a Camera, 507
• The Levy distribution’s failure to survive time aggregation cooled academic interest in fat tails #corroborates (0.75) — Donald MacKenzie, An Engine, Not a Camera, 509
• Large samples average out random variation to reveal underlying economic laws #contradicts (0.75)
• Mainstream statistics training in the 1970s ignored Levy distributions #corroborates (0.70) — Donald MacKenzie, An Engine, Not a Camera, 481