The Lambert Way to Gaussianize Heavy-Tailed Data with the Inverse of Tukey’s h Transformation as a Special Case

Figure 7

Lambert W Gaussianization of S&P 500 log-returns: . In (a) and (b): data (top left); autocorrelation function (ACF) (top right); histogram, Gaussian fit, and KDE (bottom left); Normal QQ plot (bottom right).

(a) Observed heavy tail returns

(b) Gaussianized returns