In a large hall, sound bounces off the walls, and even if you stand in a corner, you can guess the shape of the room from the echo. The same applies in science: even if you observe only a small part of a complex system, you can hear the "echo" of the main processes in its time series.
The system can be anything: an ocean, the atmosphere, a molecule. We see only one quantity, such as the temperature at a single point. Behind it lie many hidden variables. But the system has a set of Ruelle–Pollicott resonances, numbers that tell you how quickly the connections between past and future decay. You can estimate these resonances from a time series by dividing it into bins and counting how often the system moves from one bin to another.
This lets you test how well a simplified model preserves temporal correlations and find hidden oscillations in noisy data. Previously it was unclear whether this could be done; now it has been shown that it can, and it works.
Ruelle–Pollicott resonances are named after David Ruelle and Mark Pollicott, who introduced them in the mid-1980s for chaotic deterministic systems. In the stochastic context, they correspond to eigenvalues of the Kolmogorov operator, which describes the evolution of probability distributions.