Beyond long memory in heart rate variability: An approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

Leite, Argentina; Rocha, Ana Paula; Silva, Maria Eduarda

doi:10.1063/1.4802035

Cited by 24 publications

(19 citation statements)

References 33 publications

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“…Moreover, the leverage parameter estimateξ 1 , (d), changes over time and presents higher values for the healthy subject. These results are in concordance with [3,5].…”

supporting

confidence: 81%

“…The description of 24 hour HRV recordings which are long (approximately 100 000 beats) and exhibit several non stationary characteristics with circadian variation, is achieved by ARFIMA-EGARCH modeling combined with adaptive segmentation [3]: long records are decomposed into short records of variable length (≥ 512 beats) and the break points, which mark the end of consecutive short records, are identified by AIC criterion. A detailed description of the ARFIMA-EGARCH modeling procedure can be found in [5].…”

mentioning

confidence: 99%

“…The modeling of such variability can provide a quantitative and non-invasive method to assess the integrity of the cardiovascular system. HRV data display non stationarity and exhibit long memory and time-varying conditional variance (usually designated by volatility) among other nonlinear characteristics [2], that are well modelled by AutoRegressive Fractionally Integrated Moving Average (ARFIMA) models with Generalised AutoRegressive Conditional Heteroscedastic (GARCH) errors [3]. 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 [4].…”

mentioning

confidence: 99%

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Volatility Leveraging in Heart Rate: health vs disease

Rocha

Leite

Silva

2016

2016 Computing in Cardiology Conference (CinC)

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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. IntroductionHeart Rate Variability (HRV) reflects the interaction between perturbations to the cardiovascular variables and the corresponding response of the cardiovascular regulatory systems [1]. The modeling of such variability can provide a quantitative and non-invasive method to assess the integrity of the cardiovascular system. HRV data display non stationarity and exhibit long memory and time-varying conditional variance (usually designated by volatility) among other nonlinear characteristics [2], that are well modelled by AutoRegressive Fractionally Integrated Moving Average (ARFIMA) models with Generalised AutoRegressive Conditional Heteroscedastic (GARCH) errors [3]. 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 [4]. In [5] the authors consider an extension of GARCH models, Exponential GARCH (EGARCH) models, which allow for an asymmetric effect (leverage effect) and conclude that a model with leverage effect is more suited to describe the complex and nonlinear characteristics of HRV. 2.Data and Methods DataThis study analyses HRV data from the Noltisalis database [6] which was collected by the cooperative effort of university departments and rehabilitation clinics in Italy. The dataset consists of 24 hour HRV recordings of 30 subjects: 10 healthy subjects (N, 22.5 ± 1.6 hours; 102115.2 ± 11365.4 beats; 42.2 ± 6.4 years), 10 patients suffering from congestive heart failure (C, 22.4±0.9 hours; 107170.5 ± 16689.3 beats; 53.6 ± 11.2 years) and 10 heart transplanted patients (T, 22.4 ± 0.7 hours; 116043.3 ± 119...

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“…Moreover, the leverage parameter estimateξ 1 , (d), changes over time and presents higher values for the healthy subject. These results are in concordance with [3,5].…”

supporting

confidence: 81%

mentioning

confidence: 99%

mentioning

confidence: 99%

See 1 more Smart Citation

Volatility Leveraging in Heart Rate: health vs disease

Rocha

Leite

Silva

2016

2016 Computing in Cardiology Conference (CinC)

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“…The former produces fractal signals with long memory and, despite its origin in financial economics [52], it is broadly used to model anomalous diffusion in various fields of science, like atmosphere physics and geophysics [53,54], astrophysics [55], biology and physiology [56,57], and many other. The latter can be viewed as a version of a random walk in random time [58].…”

Section: Computer-generated Signalsmentioning

confidence: 99%

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations

2015

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The detrended cross-correlation coefficient ρDCCA has recently been proposed to quantify the strength of cross-correlations on different temporal scales in bivariate, non-stationary time series. It is based on the detrended cross-correlation and detrended fluctuation analyses (DCCA and DFA, respectively) and can be viewed as an analogue of the Pearson coefficient in the case of the fluctuation analysis. The coefficient ρDCCA works well in many practical situations but by construction its applicability is limited to detection of whether two signals are generally cross-correlated, without possibility to obtain information on the amplitude of fluctuations that are responsible for those cross-correlations. In order to introduce some related flexibility, here we propose an extension of ρDCCA that exploits the multifractal versions of DFA and DCCA: MFDFA and MFCCA, respectively. The resulting new coefficient ρq not only is able to quantify the strength of correlations, but also it allows one to identify the range of detrended fluctuation amplitudes that are correlated in two signals under study. We show how the coefficient ρq works in practical situations by applying it to stochastic time series representing processes with long memory: autoregressive and multiplicative ones. Such processes are often used to model signals recorded from complex systems and complex physical phenomena like turbulence, so we are convinced that this new measure can successfully be applied in time series analysis. In particular, we present an example of such application to highly complex empirical data from financial markets. The present formulation can straightforwardly be extended to multivariate data in terms of the q-dependent counterpart of the correlation matrices and then to the network representation.

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“…Politano et al (2013) discussed cross-correlation coefficients and summary statistics on heart rate and respiratory rate as they monitored the risk of intubation among STICU patients. Leite et al (2013a) applied Fractionally Integrated Autoregressive Moving Average models with Generalized Autoregressive Conditional Heteroscedastic errors (ARFIMA-GARCH) in their differentiation between normal and abnormal subjects.…”

Section: Volatility Of Physiologic Time Seriesmentioning

confidence: 99%

Preconditions and multilevel models in studying post-surgical adverse outcomes

Terner

Brown

2015

Netw Model Anal Health Inform Bioinforma

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A variety of adverse outcomes, such as kidney injury, death, cardiac injury, and respiratory failure affect a significant number of patients after surgery. Previous research has investigated possible predictors for these outcomes, including features extracted from physiologic time series, change points in the time series, and prior conditions. This study builds upon this previous work by further exploring time series statistics, such as entropy, long-term memory, and change point analysis, as possibly predictive measures of volatility. These statistics are further examined by conditioning on prior conditions using multilevel modeling. For prediction, we use both random forest models and the robust method of L 1 regularized logistic regression. Predictive results from these models are evaluated using receiver operating characteristic curves and their area under the curve values. While the developed models did not show improvements in predictive accuracy, they did show that change point analysis and measures of entropy and long-term memory can be useful tools in predicting post-surgical adverse outcomes. The multilevel models show the important interactions between prior conditions and time series statistics for predicting adverse outcomes.

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Beyond long memory in heart rate variability: An approach based on fractionally integrated autoregressive moving average time series models with conditional heteroscedasticity

Cited by 24 publications

References 33 publications

Volatility Leveraging in Heart Rate: health vs disease

Volatility Leveraging in Heart Rate: health vs disease

Detrended fluctuation analysis made flexible to detect range of cross-correlated fluctuations

Preconditions and multilevel models in studying post-surgical adverse outcomes

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