Estimation of Hierarchical Archimedean Copulas as a Shortest Path Problem

- Available estimators of high dimensional dependence structures require complete enumeration and recursive estimation of all possible alternatives.
- Hierarchical Archimedean copulas can be estimated as shortest path problems without complete enumeration.
- The estimator dominates available alternatives in terms of precision.

We formulate the problem of finding and estimating the optimal hierarchical Archimedean copula as an amended shortest path problem. The standard network flow problem is amended by certain constraints specific to copulas, which limit scalability of the problem. However, we show in dimensions as high as twenty that the new approach dominates the alternatives which usually require recursive estimation or full enumeration.