  In the framework of time series analysis with recurrence networks, we
introduce a self-adaptive method that determines the elusive recurrence
threshold and identifies metastable states in complex real-world time series.
As initial step, we introduce a way to set the embedding parameters used to
reconstruct the state space from the time series. We set them as the ones
giving the maximum Shannon entropy for the first simultaneous minima of
recurrence rate and Shannon entropy. To identify metastable states, as well as
the transitions between them, we use a soft partitioning algorithm for module
finding which is specifically developed for the case in which a system shows
metastability. We illustrate our method with two complex time series examples.
Finally, we show the robustness of our method for identifying metastable
states. Our results suggest that our method is robust for identifying
metastable states in complex time series, even when introducing considerable
levels of noise and missing data points.
