Abstract
Long-term heart rate variability (HRV) series can be described by time-variant autoregressive modelling. HRV recordings show dependence between distant observations that is not negligible, suggesting the existence of long-range correlations. In this work, selective adaptive segmentation combined with fractionally integrated autoregressive moving-average models is used to capture long memory in HRV recordings. This approach leads to an improved description of the low- and high-frequency components in HRV spectral analysis. Moreover, it is found that in the 24-h recording of a case report, the long-memory parameter presents a circadian variation, with different regimes for day and night periods.

Abstract
Heart rate variability (HRV) data display non-stationary characteristics and exhibit long-range correlation (memory). Detrended fluctuation analysis (DFA) has become a widely-used technique for long memory estimation in non-stationary HRV data. Recently, we have proposed an alternative approach based on fractional integrated autoregressive moving average (ARFIMA) models. ARFIMA models, combined with selective adaptive segmentation may be used to capture and remove long-range correlation, leading to an improved description and interpretation of tire components in 24 hour HRV recordings. In this work estimation of long memory by DFA and selective adaptive ARFIMA modelling is carried out in 24 hour HRV recordings of 17 healthy subjects of two age groups. The two methods give similar information on long-range global characteristics. However ARFIMA modelling is advantageous, allowing the description of long-range correlation in reduced length segments.

Abstract
Heart rate variability (HRV) has been used as a non-invasive marker of the activity of the autonomic nervous system and its spectrum analysis gives a measure of the sympatho-vagal balance. If short segments are used in an attempt to improve temporal resolution, autoregressive spectral estimation, where the model order must be estimated, is preferred. In this paper we compare four criteria for the estimation of the 'optimum' model order for an autoregressive (AR) process applied to short segments of tachograms used for HRV analysis. The criteria used were Akaike's final prediction error. Akaike's information criterion, Parzen's criterion of autoregressive transfer function and Rissanen's minimum description length method, and they were first applied to tachograms to verify (i) the range and distribution of model orders obtained and (ii) if the different techniques suggest the same model order for the same frames. The four techniques were then tested using a true AR process of known order p = 6: this verified the ability of the criteria to estimate the correct order of a true AR process and the effect. on the spectrum. of choosing a wrong model order was also investigated. It was found that all the four criteria underestimate the true AR orders specifying a fixed model order was then looked at and it is recommended that an AR order not less than p = 16, should be used for spectral analysis of short segments of tachograms.

Abstract
Heart rate variability (HRV) data display nonstationary characteristics, exhibit long-range correlations (memory) and instantaneous variability (volatility). Recently, we have proposed fractionally integrated autoregressive moving average (ARFIMA) models for a parametric alternative to the widely-used technique detrended fluctuation analysis, for long memory estimation in HRV. Usually, the volatility in HRV studies is assessed by recursive least squares. In this work, we propose an alternative approach based on ARFIMA models with generalized autoregressive conditionally heteroscedastic (GARCH) innovations. ARFIMA-GARCH models, combined with selective adaptive segmentation, may be used to capture and remove long-range correlation and estimate the conditional volatility in 24 hour HRV recordings. The ARFIMA-GARCH approach is applied to 24 hour HRV recordings from the Noltisalis database allowing to discriminate between the different groups.