Can Variance Gamma Distribution parameters be used as Variance Gamma Process parameters?

Can Variance Gamma Distribution parameters be used as Variance Gamma
Process parameters?

The closed form estimations the of Variance Gamma Distribution standard
deviation and kurtosis parameters are
$$\hat\sigma^2=\sum\limits_i X_i^2/N$$
and
$$\hat\nu=\{\sum\limits_i X^4_i/N\}(3\hat\sigma^4)^{-1}-1$$
Can those be used as the $\sigma$ and $\nu$ parameters for the Variance
Gamma Process? If not, do closed form estimations of those parameters from
data exist? If so, what are they?