  When evaluating the impact of a policy on a metric of interest, it may not be
possible to conduct a randomized control trial. In settings where only
observational data is available, Synthetic Control (SC) methods provide a
popular data-driven approach to estimate a "synthetic" control by combining
measurements of "similar" units (donors). Recently, Robust SC (RSC) was
proposed as a generalization of SC to overcome the challenges of missing data
high levels of noise, while removing the reliance on domain knowledge for
selecting donors. However, SC, RSC, and their variants, suffer from poor
estimation when the pre-intervention period is too short. As the main
contribution, we propose a generalization of unidimensional RSC to
multi-dimensional RSC, mRSC. Our proposed mechanism incorporates multiple
metrics to estimate a synthetic control, thus overcoming the challenge of poor
inference from limited pre-intervention data. We show that the mRSC algorithm
with $K$ metrics leads to a consistent estimator of the synthetic control for
the target unit under any metric. Our finite-sample analysis suggests that the
prediction error decays to zero at a rate faster than the RSC algorithm by a
factor of $K$ and $\sqrt{K}$ for the training and testing periods (pre- and
post-intervention), respectively. Additionally, we provide a diagnostic test
that evaluates the utility of including additional metrics. Moreover, we
introduce a mechanism to validate the performance of mRSC: time series
prediction. That is, we propose a method to predict the future evolution of a
time series based on limited data when the notion of time is relative and not
absolute, i.e., we have access to a donor pool that has undergone the desired
future evolution. Finally, we conduct experimentation to establish the efficacy
of mRSC on synthetic data and two real-world case studies (retail and Cricket).
