Semiparametric Gaussian Variance-Mean Mixtures for Heavy-Tailed and Skewed Data

Table 3

Posterior quantile estimation to show the model fitting. Posterior quantile C.I.s are obtained by simulating 200 reconstructed datasets based (each consisting of 5470 data points) on posterior samples of unknown quantities, each dataset giving one set of quantile point estimates. Real data quantiles are obtained from the 5470 observed S&P 500 returns.

Quantiles	Real data	Posterior	Posterior 95%
	quantile	mean	C.I.
2.5%	−1.965	−1.965	[−2.097, −1.867]
5%	−1.511	−1.513	[−1.589, −1.440]
25%	−0.493	−0.495	[−0.534, −0.469]
50%	−0.0315	−0.0175	[−0.0421, 0.0087]
75%	0.467	0.476	[0.440, 0.512]
95%	1.537	1.560	[1.482, 1.649]
97.5%	2.056	2.064	[1.943, 2.225]