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 m, and time lag τ, 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.