Influence of autoregressive model parameter uncertainty on spectral estimates of heart rate dynamics

Linear autoregressive (AR) model-based heart rate (HR) spectral analysis has been widely used to study HR dynamics. Owing to system and measurement noise, the parameters of an AR model have intrinsic statistical uncertainty. In this study, we evaluate how this AR parameter uncertainty can translate to uncertainty in HR power spectra. HR time series, obtained from seven subjects in supine standing positions, were fitted to AR models by least squares minimization via singular value decomposition. Spectral uncertainty due to inexact parameter estimation was assessed through a Monte Carlo study in which the AR model parameters were varied randomly according to their Gaussian distributions. Histogram techniques were used to evaluate the distribution of 50,000 AR spectral estimates of each HR time series. These Monte Carlo uncertainties were found to exceed those predicted by previous theoretical approximations. It was determined that the uncertainty of AR HR spectral estimates, particularly the locations and magnitudes of spectral peaks, can often be large. The same Monte Carlo analysis was applied to synthetic AR time series and found levels of spectral uncertainty similar to that of the HR data, thus suggesting that the results of this study are not specific to experimental HR data. Therefore, AR spectra may be unreliable, and one must be careful in assigning pathophysiological origins to specific spectral features of any one spectrum.