The disclosed embodiments relate to a system that compactly stores time-series sensor signals. During operation, the system receives original time-series signals comprising sequences of observations obtained from sensors in a monitored system. Next, the system formulizes the original time-series sensor signals to produce a set of equations, which can be used to generate synthetic time-series signals having the same correlation structure and the same stochastic properties as the original time-series signals. Finally, the system stores the formulized time-series sensor signals in place of the original time-series sensor signals.