A volcano can be considered as a dynamical system, and each time series recorded at a volcano can be interpreted as one of its observables. It is therefore theoretically possible to extract, from a single time series, information about the underlying governing system. This is done through a procedure called "embedding" that is based on the intuitive statement that the only time series available carries with it information also about the time evolution of other parameters that we are not able to sample or observe. Carrying out this embedding procedure requires estimates of key parameters such as the optimal delay time and a proper embedding dimension. Another independent, but conceptually similar procedure makes use of the Singular Spectral Analysis or Singular Value Decomposition. These and other related approaches can be used to conduct a data reduction phase, which condenses the amount of data to be analyzed and processed, while retaining the most of the information content. The resulting reduced data stream can be used for a number of purposes, such as characterizing different volcanic regimes, examining their relationship with external or internal events such as tectonic or volcano-tectonic seismic events, looking for precursors of paroxysmal eruptive phases etc. In this chapter the existing literature on this subject will be reviewed, and the prospects of future research will be discussed.
