LMSE (2017), MSE-ARFI (2019), MSE-VARFI (2020)
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].
TO VIEW AND DOWNLOAD THE LMSE TOOLBOX CLICK HERE
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].
TO VIEW AND DOWNLOAD THE ARFI-MSE TOOLBOX CLICK HERE
The approach is further extended to the multivariate case to compute multiscale entropy and information storage in the presence of long-range correlations and multiple time series. This is achieved by extending the formulation to the analysis of vector AR fractionally-integrated (VARFI) models; this extension is presented in Ref. [3].
TO VIEW AND DOWNLOAD THE MSE-VARFI TOOLBOX CLICK HERE
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; 99:032115. DOI:10.1103/PhysRevE.99.032115
[3] A Martins, R Pernice, C Amado, AP Rocha, ME Silva, M Javorka, L Faes, 'Multivariate and Multiscale Complexity of Long-Range Correlated Cardiovascular and Respiratory Variability Series', Entropy, 2020