Algorithm 2 Data preprocessing to isolate and transform data exhibiting extreme behavior. $r_i$ represents the radial component, and ${\mathit{v}}_i$ the angular component. The declustering portion is relevant for data correlated in time.

for  $\mathsf{\ell }=1,\dots ,d$  do     Set $b_{t,\mathsf{\ell }}={\widehat{F}}_{\mathsf{\ell }}^{-1}\left(1-\frac{1}{t}\right)$.     With ${\mathit{x}}_{\mathsf{\ell }}>b_{t,\mathsf{\ell }}$, fit ${\sigma }_{\mathsf{\ell }}$, ${\xi }_{\mathsf{\ell }}$ via MLE according to generalized Pareto likelihood. end for for  $i=1,\dots ,n$  do     Define $z_{i,\mathsf{\ell }}={\left(1+{\xi }_{\mathsf{\ell }}\frac{x_{i,\mathsf{\ell }}-b_{t,\mathsf{\ell }}}{{\sigma }_{\mathsf{\ell }}}\right)}_{+}^{1/{\xi }_{\mathsf{\ell }}}$;      then $r_i={∥{\mathit{z}}_i∥}_{\infty }$, ${\mathit{v}}_i=\frac{{\mathit{z}}_i}{{∥{\mathit{z}}_i∥}_{\infty }}$ end for Subset $\mathit{r},\mathit{v}$ such that $r_i\ge 1$ if declustering then     for $i=1,\dots ,n$ do         If $r_i\ge 1$ and $r_{i-1}\ge 1$, drop the lesser (and associated $v_i$) from dataset.     end for end if