  We seek to extract a small number of representative scenarios from large and
high-dimensional panel data that are consistent with sample moments. Among two
novel algorithms, the first identifies scenarios that have not been observed
before, and comes with a scenario-based representation of covariance matrices.
The second proposal picks important data points from states of the world that
have already realized, and are consistent with higher-order sample moment
information. Both algorithms are efficient to compute, and lend themselves to
consistent scenario-based modeling and high-dimensional numerical integration.
Extensive numerical benchmarking studies and an application in portfolio
optimization favor the proposed algorithms.
