LMSE and MSE-ARFI - Matlab Tools for the computation of
Linear Multiscale Entropy and Information Storage


The most common approach to assess the dynamical complexity of a time series across multiple temporal scales makes use of the multiscale entropy (MSE) and refined MSE (RMSE) measures. In spite of their popularity, MSE and RMSE lack of an analytical framework allowing their calculation for known dynamic processes, and cannot be reliably computed over short time series.


To overcome these limitations, we propose a method to assess RMSE for autoregressive (AR) stochastic processes. The method makes use of linear state space (SS) models to provide the multiscale parametric representation of an AR process observed at different time scales, and exploits the SS parameters to quantify analytically the complexity of the process. This method is presented in ref. [1].

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Moreover, the approach is extended to compute the information storage and, importantly, to account for the effect of long-range correlations. This is achieved by extending the formulation to the analysis of AR fractionally-integrated (ARFI) models  this extension is presented in Ref. [2].

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References:

[1] L Faes, A Porta, M Javorka, G Nollo, 'Efficient computation of multiscale entropy over short biomedical time series based on linear state-space models', Complexity, 2017; 2017:1768264 (13 pages). DOI: 10.1155/2017/1768264

[2] L Faes, MA Pereira, ME Silva, R Pernice, A Busacca, M Javorka, AP Rocha, 'Multiscale information storage of linear long-range correlated stochastic processes', Physical review E, 2019; in press