A differential entropy based method for determining the optimal embedding parameters of a signal

A novel method for determining the set of parameters for a phase space representation of a time series is proposed. Based upon the differential entropy, both the optimal embedding dimension , and time lag , are simultaneously determined. The choice of these parameters is closely related to the length of the optimal tap input delay line of an adaptive filter or time-delay neural network. The method employs a single criterion – the “entropy ratio” between the phase space representation of a signal and an ensemble of its surrogates – and is first systematically tested on synthetic time series for which the optimal embedding parameters are known, after which it is verified on a number of benchmark real-world time series. The proposed entropy ratio method is shown to consistently outperform some well-established methods.