Mandelbrot read Houthakker’s cotton price data as evidence of volatility clustering contradicting normal distributions.

Evidence

On Houthakker’s blackboard were data about changes in the price of cotton. What Mandelbrot-champion of the role of the “eye” in science saw in Houthakker’s data was a sign of his monsters, indications of the joint distribution of two Levy variables (figure 4.1) that exhibited a particular form of dependence. In the latter, if the two variables indicate the changes in prices in two successive time intervals, “large changes tend to be followed by large changes of either sign and small changes tend to be followed by small changes” (Mandelbrot 1963a, p. 418). If we were in the non-monstrous world of the normal distribution, the “probability isolines” of the joint distribution would be circles or ellipses. Instead, in Houthakker’s data, Mandelbrot saw the cross-shaped isolines of figure 4. 1: the mark, to his eye, of his monsters. — Donald MacKenzie, An Engine, Not a Camera, 486

Categorization

• XREF: Volatility clustering — large changes followed by large changes of either sign — prefigures the now-standard ARCH/GARCH literature in empirical finance. — connects to: Mandelbrot’s cotton price analysis routed him into the mainstream topic of price change distributions. — Donald MacKenzie, An Engine, Not a Camera: How Financial…, 488
• SEED: The role of visual pattern recognition (‘the eye’) in discovering statistical structure is an essay angle on tacit scientific craft vs. formal testing.

Broader Connections

• Mandelbrot’s cotton price analysis routed him into the mainstream topic of price change distributions. #expands (0.85) — Donald MacKenzie, An Engine, Not a Camera, 488