How to compute suitable vicinity parameter and sampling time of recurrence analysis

Abstract We show how the maximum of recurrence-mi\-cro\-states entropy configures a new way to properly compute appropriate recurrence vicinity parameter and time sampling to perform recurrence analysis of continuous data. For experimental data, we show the same procedure may be used to find the optimum sampling or to perform down-sampling of the data, preserving recurrence meaning and adjusting the ideal sampling. The new method retrieves results obtained using traditional methods with the advantage of being independent of any free parameter, since all parameter dependencies are automatically set. Our results are also less sensitive to noise when experimental data is used. Due to the automatized way to capture suitable recurrence parameters, the method is adequate for using in autonomous numerical algorithms, allowing the recovery of relevant recurrence information embedded in time series (including over-sampled data), rationalizing the process of data acquisition and allowing only relevant data to be collected.