  Uncertainty quantification is a fundamental problem in the analysis and
interpretation of synthetic control (SC) methods. We develop conditional
prediction intervals in the SC framework, and provide conditions under which
these intervals offer finite-sample probability guarantees. Our method allows
for covariate adjustment and non-stationary data. The construction begins by
noting that the statistical uncertainty of the SC prediction is governed by two
distinct sources of randomness: one coming from the construction of the (likely
misspecified) SC weights in the pre-treatment period, and the other coming from
the unobservable stochastic error in the post-treatment period when the
treatment effect is analyzed. Accordingly, our proposed prediction intervals
are constructed taking into account both sources of randomness. For
implementation, we propose a simulation-based approach along with
finite-sample-based probability bound arguments, naturally leading to
principled sensitivity analysis methods. We illustrate the numerical
performance of our methods using empirical applications and a small simulation
study. \texttt{Python}, \texttt{R} and \texttt{Stata} software packages
implementing our methodology are available.
