I have been working on non linear time series analysis using complex systems theory. Currently I am using recurrence plots to analyze recurrences and also performing recurrence quantification analysis (RQA) to find how long the state of the system is locked in recurrence.
Let's say we have a time series $X_1$, through recurrence plots I make a record of the time periods $X_1$ stayed in recurrence, at particular states. So, for phase space regions $S_1, S_2, S_3...$ I have time periods of recurrence $t_1, t_2, t_3...$, respectively. Now, is there a way of looking into predicting phase transitions or methods like early warning signals so that I can predict phase transitions to states I have a record of? I also want to predict how long the time series is likely to stay around that state.
Is this possible? If so, how?