MSE-ARFI - Matlab Tool for the computation of
Multiscale Entropy and Information Storage in linear processes with long range correlations

Information storage, reflecting the capability of a dynamical system to keep predictable information during its evolution over time, is a key element of intrinsic distributed computation, useful for the description of the dynamical complexity of several physical and biological processes. Here we introduce a parametric approach which allows one to compute information storage across multiple timescales in stochastic processes displaying both short-term dynamics and long-range correlations (LRC). Our approach makes use of linear fractionally integrated autoregressive (ARFI) models to derive
analytical expressions for the information storage computed at multiple timescales.

The MSE-ARFI Matlab toolbox reproduces algorithms, simulations and real data analysis reported in [1].



[1] 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


Zip file with all scripts and functions:

The code is provided free of charge. It is neither exhaustively tested nor particularly well documented. The authors accept no liability for its use. Use, modification and redistribution of the code is allowed in any way users see fit. Authors ask only that authorship is acknowledged and ref. [1] is cited upon utilization of the code in integral or partial form.

DISCLAIMER OF WARRANTIES AND LIMITATION OF LIABILITY The code is supplied as is and all use is at your own risk. The authors disclaim all warranties of any kind, either express or implied, as to the softwares, including, but not limited to, implied warranties of fitness for a particular purpose, merchantability or non - infringement of proprietary rights. Neither this agreement nor any documentation furnished under it is intended to express or imply any warranty that the operation of the software will be error - free. Under no circumstances shall the authors of the softwares provided here be liable to any user for direct, indirect, incidental, consequential, special, or exemplary damages, arising from the software, or user' s use or misuse of the softwares. Such limitation of liability shall apply whether the damages arise from the use or misuse of the data provided or errors of the software.

To get started, we recommend that you run and work through the demonstration script.

- ar2arfi.m: generation of ARFI polynomial from AR polynomial and differencing parameter
- ar2mse.m: computes LMSE at a given scale (s/tau) from assigned AR parameters
- d_estimation.m: returns an estimate of the differencing parameter d (Whittle semiparametric estimator)
- idMVAR.m: AR process identification (from eMVAR toolbox)
- iss_ds.m: computes innovations form SS parameters for a downsampled SS model
- iss_PV: computes partial variances for a state space model from innovations form SS parameters
- mos_idMVAR.m AR process order selection (from eMVAR toolbox)
- remove_d.m: filters a time series based on the differencing parameter d to remove long-range correlations
- ss2iss.m: computes innovations form SS parameters from SS parameters
- varma2iss.m: computes innovations form SS parameters from VARMA parameters

- MSE_ARFI_estimation.m: computation of information storage and multiscale entropy using the three approaches considered in [1]:
a) AR estimates from linear-detrended data
b) AR estimates from data filtered with the differencing parameter d to remove long-range correlations
c) ARFI estimates on the original data

- in the directory \series, four examples of cardiovascular time series analyzed in [1] (systolic arterial pressure, RR intervals, respiration time series for subjects in the resting supine condition and in the upright condition during head-up tilt)

NOTE: the iss_ds and ss2iss functions are taken from the State-Space Granger Causality Matlab Toolbox  -