Ni hao Chengyu Liu, 

Entropy measures for time series, such as sample entropy (SampEn) and approximated entropy (ApEn, Pincus & Goldberger, 1994) do indeed measure the unpredictability (opposite of regularity) of a time series. In short, they measure how much a given data point depends on the values of a number m of previous data points, averaged over the whole time series. In literature, there has been some confusion on the relation between entropy and complexity/variability/regularity/predictabiltiy, see e.g. the discussion by Goldberger et al. (2002). 

More recently, Costa et al. (2002, 2005) have proposed a new entropy-based measure for time series that seems to quantify complexity better, and have coined it Multiscale Entropy (MSE). Basically, it is nothing else than applying SampEn or ApEn to different coarse-grained versions of the time series (i.e. copies of the original time series at different resolutions, or different time scales) and then plotting the entropy value in function of the time scale. The method appears to work magically well, has been applied to cardiac, encephalographic and other physiological time series, and the two papers have been cited already more than 700 and 500 times, respectively. I've just started to work with MSE, and I'm using some free and easy-to-use MATLAB-based software from the Psynet group. If you prefer C, then there's the free software developped by Costa et al. that you can download from Physionet. 

I hope this comment can help you, best regards, 

Ruben. 

Costa, Goldberger & Peng (2002). "Multiscale Entropy Analysis of Complex Physiologic Time Series". Phys. Rev. Lett 89, 068102-.

Costa, Goldberger & Peng (2005). "Multiscale entropy analysis of biological signals", Phys. Rev. E 71, 2005.

Goldberger, Peng & Lipsitz (2002). "What is physiologic complexity and how does it change with aging and disease?". Neurobiol. Aging 23, 23.

Pincus & Goldberger (1994). "Physiological time-series analysis: what does regularity quantify?", Am. J. Physiol. 266, H1643. 

Psynet: Initiative of Nonlinear Dynamics in Psychiatry [ http://www.psynetresearch.org/ ]

Physionet [ http://www.physionet.org/ ]

Ni hao Chengyu Liu, 

Entropy measures for time series, such as sample entropy (SampEn) and approximated entropy (ApEn, Pincus & Goldberger, 1994) do indeed measure the unpredictability (opposite of regularity) of a time series. In short, they measure how much a given data point depends on the values of a number m of previous data points, averaged over the whole time series. In literature, there has been some confusion on the relation between entropy and complexity/variability/regularity/predictabiltiy, see e.g. the discussion by Goldberger et al. (2002). 

More recently, Costa et al. (2002, 2005) have proposed a new entropy-based measure for time series that seems to quantify complexity better, and have coined it Multiscale Entropy (MSE). Basically, it is nothing else than applying SampEn or ApEn to different coarse-grained versions of the time series (i.e. copies of the original time series at different resolutions, or different time scales) and then plotting the entropy value in function of the time scale. The method appears to work magically well, has been applied to cardiac, encephalographic and other physiological time series, and the two papers have been cited already more than 700 and 500 times, respectively. I've just started to work with MSE, and I'm using some free and easy-to-use MATLAB-based software from the Psynet group. If you prefer C, then there's the free software developped by Costa et al. that you can download from Physionet. 

I hope this comment can help you, best regards, 

Ruben. 

Costa, Goldberger & Peng (2002). "Multiscale Entropy Analysis of Complex Physiologic Time Series". Phys. Rev. Lett 89, 068102-.

Costa, Goldberger & Peng (2005). "Multiscale entropy analysis of biological signals", Phys. Rev. E 71, 2005.

Goldberger, Peng & Lipsitz (2002). "What is physiologic complexity and how does it change with aging and disease?". Neurobiol. Aging 23, 23.

Pincus & Goldberger (1994). "Physiological time-series analysis: what does regularity quantify?", Am. J. Physiol. 266, H1643. 

Psynet: Initiative of Nonlinear Dynamics in Psychiatry [ http://www.psynetresearch.org/ ]

Physionet [ http://www.physionet.org/ ]

Dear Ruben Fossion,

Thank you very much for your kind helps on this question. I very appraciate it. The references you suggested are also helpful.

I agree with that the tranditional Entropy measures (ApEn, SampEn and FuzzyEn) usually maximize the random time series rather than nonlinear time series. For the physiological applicaitons (such as cardiovacular time series), one fundamental hypothesis is that healthy subjects have more complicate time series than cardiovascular patients. so  we want the Entropy measure has higher value for more complicate time series.

So if it is need to develop an algorithm, which could obtain maximum entropy values for nonlinear signals, has middle values for random signals and has minimum values for periodic signals?

Many thanks.

Entropy: A concept that is not a physical quantity

https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity

Dear Prof. Liu,

Shannon Entropy can be derived in a electronic stock market model endogenously whther the markets are in systems equilibrium or not. This is an aside of the result I obtained in my PhD thesis at NYU Economics Dept. in the GSAS in 1993 (Prof. Yaw Nyarko, Prof. Andrew Schotter, Prof. Aldo Rustichini, Prof. Christopher Flinn) committee members. This in its exact form requires a logarithmic utility specification for the state preference approach capital assets pricing model with industrial categories (mathematical-statistically) which follows from the bounded rational Arrow-Debreu specification. This model gave me my PhD and has been copyrighted by the Library of Congress. So I have high hopes for it. If not anything as the start of Management Engineering Econophysics Field. In it I had derived why efficiency measurements in the physical space of stock markets require extended measurement than is currently being done with electronic cross-bar type telephonic stock exchanges where quotes are matched in stock and flow fashion of quantum Econophysics (Mallick, Hamburger, Mallick (2016, 2017, 2018)) and shares flow through the price sigalling mechanism and trade wavelates are created with functor algebra categories in closed sets of quantum fluctuations over spacextime. The dynamics follows RHMHM Functor Algebra Calculus thereby obeying methodological mechanics. So I think the Laws of Electrodynamics are obeyed in this cybernetic closed syste m in spacextime.

Soumitra K. Mallick

for Soumitra K. Mallick, Somak Raychaudhury, Sandipan Mallick

for RHMHM School,

USA, Japan, India