Luca Faes

ARres - Matlab Tool for Computing Confidence Limits of Measures derived from Autoregressive Modeling of Time Series

In the assessment of physiological function, statistical tests are ubiquitous. Most commonly these focus on the average behaviour of a group of subjects, and assess distributions and significant changes across tasks or between groups of subjects, considering the variability between individuals as a random/confounding effect. However, in several experimental/clinical applications, the focus should be on the individual subject, to determine confidence limits of estimates and to test for significant changes as a result of experimental procedures, or other factors. To this end we introduce a method for computing confidence limits and perform statistical comparison for parameters derived from autoregressive AR models applied to a single time series, which exploits Monte Carlo or Bootstrap approaches.

The toolbox provides Matlab functions to compute several resampled realizations of the AR parameters (first estimated using least squares (idAR.m)) based on Monte Carlo resampling (idARres.m) or bootstrapping of the AR residuals (idARboot.m, to be used with the built-in function bootstrp.m), from which Confidence limits for AR-based indexes can be computed from individual time series. Examples of indexes to which the procedures are applied are measures of frequency and spectral power obtained from AR spectral decomposition (asd_ARMASpectDec.m), and measures of information storage or complexity obtained from information decomposition (its_CElinVAR1.m). The toolbox is demonstrated on simulations of a five-order AR process resempling spectral properties of heart rate variability time series (SimuConfLim.m).

The toolbox is based on the paper:

Beda A, Simpson DMS and Faes L, 'Estimation of Confidence Limits for Descriptive Indexes Derived from Autoregressive Analysis of Time Series: Methods and Application to Heart Rate Variability', submitted, 2016.

DOWNLOAD:

Zip file with all scripts and functions: ARres.zip

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