Linear time series analysis of long term fetal heart rate variability patterns

Long term fetal heart rate variability (LFHRV) is equivalent to detrended (when the time series trend removed) indirectly derived averaged fetal heart rate (FHR) time series. Up to now LFHRV is looked for visually in FHR traces, by obstetricians and midwifes for determination of fetal condition. The detrended averaged FHR data or LFHRV data is a random correlated non-stationary (in second moment) time series. In this paper we have applied linear stochastic time series analysis technique to identify a parsimonious stochastic model, for parametric numerical representation of the random cyclical patterns observed in short 2 minutes quasi-stationary contiguous blocks of LFHRV data. The parametric estimation technique used is based upon the optimum exact Maximum likelihood estimation (which uses Kalman filtering as part of its implementation). Diagnostics performed on the residuals indicated that a second order autoregressive model is a statistically adequate model in capturing variability patterns observed in 2 minute data windows of detrended average FHR. Also through further analysis of the spectral behavior of this identified model, pseudo-periodicity (or random periodicity) which for a long time was visually detected, can now be detected via this numerical procedure.