“The baseball announcer has it, of course, conveniently all wrong. Ted Williams is due to hit because he hasn’t hit for seven days. That’s red noise. Ted Williams is hot, he’s sure to hit tomorrow because he’s been hitting for seven days. That’s blue noise. The better description of an efficient market with random movements, which is white noise, is in between.” —
Samuelson's designation of red and blue noise is the opposite of the engineering convention for red and blue noise. The words aren't arbitrary: by analogy to visible light, red noise has enhanced low-frequency content, blue noise has enhanced high-frequency content. The hot-hand condition (positive correlation) enhances low-frequency content but Samuelson calls this blue; regression-to-the-mean (negative correlation) enhances high-frequency content but Samuelson calls it red. Are the engineering and economics definitions of red and blue noise really opposite? See, for example: https://cran.r-project.org/web/packages/colorednoise/vignettes/noise.html
Paul Samuelson's Flavors of Randomness (2004)
Samuelson's designation of red and blue noise is the opposite of the engineering convention for red and blue noise. The words aren't arbitrary: by analogy to visible light, red noise has enhanced low-frequency content, blue noise has enhanced high-frequency content. The hot-hand condition (positive correlation) enhances low-frequency content but Samuelson calls this blue; regression-to-the-mean (negative correlation) enhances high-frequency content but Samuelson calls it red. Are the engineering and economics definitions of red and blue noise really opposite? See, for example: https://cran.r-project.org/web/packages/colorednoise/vignettes/noise.html