Given a collection of MTS, the function returns the pairwise distance matrix,
where the distance between two MTS \(\boldsymbol X_T\) and \(\boldsymbol Y_T\) is defined as
$$d_{QCF}(\boldsymbol X_T, \boldsymbol Y_T)=\Bigg(\sum_{l=1}^{L}\sum_{i=1}^{r}\sum_{i'=1}^{r}\sum_{j_1=1}^{d}
\sum_{j_2=1}^{d}\bigg(\widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(l,\tau_i,\tau_{i^\prime})-\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}
(l,\tau_i,\tau_{i^\prime})\bigg)^2+$$
$$\sum_{i=1}^{r}\sum_{i'=1}^{r}\sum_{{j_1,j_2=1: j_1 > j_2}}^{d}
\bigg(\widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(0,\tau_i,\tau_{i^\prime})-
\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}(0,\tau_i,\tau_{i^\prime})\bigg)^2\Bigg]^{1/2},$$
where \(\widehat \gamma_{j_1,j_2}^{\boldsymbol X_T}(l,\tau_i,\tau_{i^\prime})\) and
\(\widehat \gamma_{j_1,j_2}^{\boldsymbol Y_T}(l,\tau_i,\tau_{i^\prime})\) are estimates of the quantile cross-covariances
with respect to the variables \(j_1\) and \(j_2\) and probability levels \(\tau_i\) and \(\tau_{i^\prime}\) for
series \(\boldsymbol X_T\) and \(\boldsymbol Y_T\), respectively.