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

Heart rate variability (HRV) analysis is widely used to investigate the autonomic regulation of the cardiovascular system. HRV is often analyzed using RR time series, which can be affected by different types of artifacts. Although there are several artifact correction methods, there is no study that compares their performances in actual experimental contexts. This work aimed to evaluate the impact of different artifact correction methods on several HRV parameters. Initially, 36 ECG recordings of control rats or rats with heart failure or hypertension were analyzed to characterize artifact occurrence rates and distributions, to be mimicked in simulations. After a rigorous analysis, only 16 recordings ( n = 16) with artifact-free segments of at least 10,000 beats were selected. RR interval losses were then simulated in the artifact-free (reference) time series according to real observations. Correction methods applied to simulated series were deletion, linear interpolation, cubic spline interpolation, modified moving average window, and nonlinear predictive interpolation. Linear (time- and frequency-domain) and nonlinear HRV parameters were calculated from corrupted-corrected time series, as well as for reference series to evaluate the accuracy of each correction method. Results show that NPI provides the overall best performance. However, several correction approaches, for example the simple deletion procedure, can provide good performance in some situations, depending on the HRV parameters under consideration. NEW & NOTEWORTHY This work analyzes the performance of some correction techniques commonly applied to the missing beats problem in RR time series. From artifact-free RR series, spurious values were inserted based on actual data of experimental settings. We intend our work to be a guide to show how artifacts should be corrected to preserve as much as possible the original heart rate variability properties.

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PEMODELAN AUTOREGRESSIVE FRACTIONALLY INTEGRATED MOVING AVERAGE DENGAN EFEK EXPONENTIAL GARCH (ARFIMA-EGARCH) UNTUK PREDIKSI HARGA BERAS DI KOTA SEMARANG

Jurnal Gaussian ◽

10.14710/j.gauss.v10i2.29933 ◽

2021 ◽

Vol 10 (2) ◽

pp. 279-292

Author(s):

Rezky Dwi Hanifa ◽

Mustafid Mustafid ◽

Arief Rachman Hakim

Keyword(s):

Time Series ◽

Long Memory ◽

Time Series Data ◽

Moving Average ◽

Financial Data ◽

Series Data ◽

Leverage Effect ◽

Standard Equipment ◽

Conditional Heteroscedasticity ◽

Auto Regressive

Time series data is a type of data that is often used to estimate future values. Long memory phenomenon often occurs in time series data. Long memory is a condition that shows a strong correlation between observations even though they are quite far away. This phenomenon can be overcome by modeling time series data using the Autoregressive Fractional Integrated Moving Average (ARFIMA) model. This model is characterized by a fractional difference value. ARFIMA (Autoregressive Fractional Integrated Moving Average) model assumes that the residuals are normally distributed, mutually independent, and homogeneous. However, usually in financial data, the residual variants are not constant. This can be overcome by modeling variants. Standard equipment that can be used to model variants is the ARCH / GARCH (Auto Regressive Conditional Heteroscedasticity / Generalized Auto Regressive Conditional Heteroscedasticity) model. Another phenomenon that often occurs in GARCH models is the leverage effect on the residuals of the model. EGARCH (Exponential General Auto Regessive Conditional Heteroscedasticity) is a development of the GARCH model that is appropriate for data that has an leverage effect. The implementation of this model is by modeling financial data, so this study takes 136 monthly data on rice prices in Semarang City from January 2009 to April 2020. The purpose of this study is to create a long memory data forecasting model using the Exponential method. Generalized Autoregressive Conditional Heteroscedasticity (EGARCH). The best model obtained is ARFIMA (1, d, 1) EGARCH (1,1) which is capable of forecasting with a MAPE value of 3.37%.Keyword : Rice price, forecasting , long memory, leverage effect, GARCH, EGARCH

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