Volatility leveraging in heart rate: Health vs disease

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. GARCHmod-els 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.