ECG Signal Modeling Using Volatility Properties: Its Application in Sleep Apnea Syndrome

Abstract

This study presents and evaluates the mathematical model to estimate the mean and variance of single-lead ECG signals in sleep apnea syndrome. Our objective is to use the volatility property of the ECG signal for modeling. ECG signal is a stochastic signal whose mean and variance are time-varying. So, we propose to decompose this nonstationarity into two additive components; a homoscedastic Autoregressive Integrated Moving Average (ARIMA) and a heteroscedastic time series in terms of Exponential Generalized Autoregressive Conditional Heteroskedasticity (EGARCH), where the former captures the linearity property and the latter the nonlinear characteristics of the ECG signal. First, ECG signals are segmented into one-minute segments. The heteroskedasticity property is then examined through various tests such as the ARCH/GARCH test, kurtosis, skewness, and histograms. Next, the ARIMA model is applied to signals as a linear model and EGARCH as a nonlinear model. The appropriate orders of models are estimated by using the Bayesian Information Criterion (BIC). We assess the effectiveness of our model in terms of mean square error (MSE), root mean square error (RMSE), mean absolute error (MAE), and mean absolute percentage error (MAPE). The data in this article is obtained from the Physionet Apnea-ECG database. Results show that the ARIMA-EGARCH model performs better than other models for modeling both apneic and normal ECG signals in sleep apnea syndrome.

A Review of Methods and Applications for a Heart Rate Variability Analysis

“…The parametric models refer to the techniques that need some parameters to be specified before becoming eligible for making predictions [55]. A number of parametric modelling approaches, including autoregressive (AR), moving average (MA), autoregressive moving average (ARMA), and autoregressive integrated moving average (ARIMA), have been proposed for the analysis of RR intervals [56]. AR, MA, and ARMA models have been used to analyze RR intervals of a small duration (e.g., 5 s) [57].…”

“…The stationarity of the RR intervals is usually verified using techniques like Augmented Dickey-Fuller (ADF). On the other hand, models like ARIMA have been suggested for the relatively longer RR intervals, which are nonstationary [56].…”

Modelling finite time-series signals using closed form solutions for first zero crossing of the Sample Autocorrelation

“…Since the noise w k is assumed to be uncorrelated with the process, the mixed terms in (9), that is 1…”

“…As i increases, the l zc of the deterministic signal y dk shifts towards lower lag values as tabulated in Table I for i = [1,9]. The range of l zc indicative of the particular model order i for the corresponding stochastic process y sk is also listed in this Table . For a particular i, this value is considered to vary from the mid-value of the deterministic l zc of i − 1 and i orders to that of i and i + 1 orders.…”

“…Various classes of time-series models, namely autoregressive (AR), moving-average (MA) and mixed autoregressive-moving-average (ARMA) models, have been derived for these signals using the ACF [2]. In particular, ACF has been used to identify the order of the time-domain models [6] for speech signals [7], [8], electrocardiogram (ECG) signals [2], [9], heart rate variability (HRV) models [10] as well as Electroencephalogram (EEG) and Electromyogram (EMG) signals [11].…”