Abstract
Heart Rate Variability (HRV) data exhibit long memory and time-varying conditional variance (volatility). These characteristics are well captured using Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalised AutoRegressive Conditional Heteroscedastic (GARCH) errors, which are an extension of the AR models usual in the analysis of HRV. GARCH models assume that volatility depends only on the magnitude of the shocks and not on their sign, meaning that positive and negative shocks have a symmetric effect on volatility. However, HRV recordings indicate further dependence of volatility on the lagged shocks. This work considers Exponential GARCH (EGARCH) models which assume that positive and negative shocks have an asymmetric effect (leverage effect) on the volatility, thus better copping with complex characteristics of HRV. ARFIMA-EGARCH models, combined with adaptive segmentation, are applied to 24 h HRV recordings of 30 subjects from the Noltisalis database: 10 healthy, 10 patients suffering from congestive heart failure and 10 heart transplanted patients. Overall, the results for the leverage parameter indicate that volatility responds asymmetrically to values of HRV under and over the mean. Moreover, decreased leverage parameter values for sick subjects, suggest that these models allow to discriminate between the different groups.

Abstract
The characterization of heart rate variability (HRV) series has become important for clinical diagnosis. These series are non-stationary and exhibit long and short-range correlations. The non-parametric methodology detrended fluctuation analysis (DFA) has become widely used for the detection of these correlations. The standard procedure is to apply DFA to the RR series, estimating the desired scaling exponents. In this work we pursue an alternative approach which consists in applying DFA to the fractionally differenced RR series, Delta(RR)-R-d, where 0 < d < 1 is the long-range correlation parameter. Both methodologies are applied to 24 hour HRV series from the Noltisalis data base. We conclude that changes in HRV are better quantified by DFA scaling exponents calculated over fractionally differenced RR series than by the standard procedure. The results indicate that the scaling exponent corresponding to high frequencies obtained from Delta(RR)-R-d increases the discriminatory power among the groups: from 60% to 87% during the day period and 57% to 77% during the night period.

Abstract
This study aimed to find parameters to characterize heart rate variability (HRV) and discriminate healthy subjects and patients with heart diseases. The parameters used for discrimination characterize the different components of HRV memory (short and long) and are extracted from HRV recordings using parametric as well as non parametric methods. Thus, the parameters are: spectral components at low frequencies (LH) and high frequencies (HF) which are associated with the short memory of HRV and the long memory parameter (d) obtained from autoregressive fractionally integrated moving average (ARFIMA) models. In the non parametric context, short memory (a1) and long memory (a2) parameters are obtained from detrended fluctuation analysis (DFA). The sample used in this study contains 24-hour Holter HRV recordings of 30 subjects: 10 healthy individuals, 10 patients suffering from congestive heart failure and 10 heart transplanted patients from the Noltisalis database. It was found that short memory parameters present higher values for the healthy individuals whereas long memory parameters present higher values for the diseased individuals. Moreover, there is evidence that ARFIMA modeling allows the discrimination between the 3 groups under study, being advantageous over DFA.

Abstract
Heart Rate Variability (HRV) series exhibit long memory and time-varying conditional variance. This work considers the Fractionally Integrated AutoRegressive Moving Average (ARFIMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. ARFIMA-GARCH models may be used to capture and remove long memory and estimate the conditional volatility in 24 h HRV recordings. The ARFIMA-GARCH approach is applied to fifteen long term HRV series available at Physionet, leading to the discrimination among normal individuals, heart failure patients, and patients with atrial fibrillation. (C) 2013 AIP Publishing LLC

Abstract
Dysfunctions of the autonomic nervous system in critically ill patients with Acute Brain Injury (ABI) lead to changes in Heart Rate Variability (HRV) which appear to be particularly marked in patients subsequently declared in Brain Death (BD). HRV series are non-stationary, exhibit long memory in the mean and time-varying conditional variance (volatility), characteristics that are well modeled by AutoRegressive Fractionally Integrated Moving Average (ARFIMA) models with Generalized AutoRegressive Conditional Heteroscedastic (GARCH) errors. The long memory is estimated by the parameter d of the ARFIMA-GARCH model, whilst the time-varying conditional variance parameters, u and v characterize, respectively, the short-range and the persistence in the conditional variance. In this work, the ARFIMA-GARCH approach is applied to HRV series of 15 pediatric patients with ABI admitted in a pediatric intensive care unit, 5 of which has BD confirmed and 9 patients survived. The long memory and time-varying conditional variance parameters estimated by ARFIMA-GARCH modeling significantly differ between groups and seem able to contribute to characterize disease severity in children with ABI.

Abstract
Long recordings of heart rate variability (HRV) display non-stationary characteristics and exhibit long- and short-range correlations. The nonparametric methodology detrended fluctuation analysis (DFA) has become a widely used technique for the detection of long-range correlations in non-stationary HRV data. Recently, we have proposed an alternative approach based on fractional integrated autoregressive moving average (ARFIMA) modelling. These models are an extension of the AR models usual in HRV analysis and have special interest for applications because of their ability for modelling both short- and long-term behaviour of a time series. In this work, DFA is used to assess also short-range scales, further characterizing the data. The methods are applied to 24 h HRV recordings from the Noltisalis database, collected from healthy subjects, patients suffering from congestive heart failure and heart transplanted patients. The analysis of short-range scales leads to a better discrimination between the different groups. © 2013, Springer-Verlag Berlin Heidelberg.