MGHDMaximal Globally Hyperbolic Development
MGHDMultivariate Generalized Hyperbolic Distributions (mathematics)
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The diagnosis of mGHD was questioned by several authors [9,13].
[26] about 15% of them continue to have mGHD and exhibit changes in body composition after therapy cessation similar to those seen in children with sGHD, although less marked.
In contrast our results indicate that mGHD has no significant influence on body composition in the short statured children.
Y ~ MGHD ([lambda], [chi], [psi], B[mu], B[SIGMA] + b, B[gamma]).
Therefore, an identification problem arises when starting to fit the parameters of the MGHD to data.
Note that further properties of the MGHD can be found in [19].
(ii) When [lambda] = 1, one can obtain a MGHD whose univariate marginal distributions are hyperbolic.
From Table 5 we also note that the result obtained for the log-likelihood and the AIC of the MSt and MGHD are very similar, although the MSt has less parameters.
(v) Finally, we fit the MGHD to both the pair of principal components derived from the price data, as well as to set of seven stock return components which are not explained by shared exogenous drivers.
We obtain the following MGHD parameters estimates for the joint return distribution of the two principal components:
We assessed the fit of the MGHD and multivariate normal models to the residuals obtained from the regression of the seven stocks against the two principal components.
It was found that it was possible to fit MGHD models to joint returns, with this model narrowly outperforming the multivariate Student's t-distribution with the next best fit.