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This study aims to identify the most significant features in physiological signals representing a biphasic pattern in the menstrual cycle using circular statistics which is an appropriate analytic method for the interpretation of data with a periodic nature. The results can be used empirically to determine menstrual phases. A non-uniform pattern was observed in ovulating subjects, with a significant periodicity (p$<$0.05) in mean temperature, heart rate (HR), Inter-beat Interval (IBI), mean tonic component of Electrodermal Activity (EDA), and signal magnitude area (SMA) of the EDA phasic component in the frequency domain. In contrast, non-ovulating cycles displayed a more uniform distribution (p$>$0.05). There was a significant difference between ovulating and non-ovulating cycles (p$<$0.05) in temperature, IBI, and EDA but not in mean HR. Selected features were used in training an Autoregressive Integrated Moving Average (ARIMA) model, using data from at least one cycle of a subject, to predict the behavior of the signal in the last cycle. By iteratively retraining the algorithm on a per-day basis, the mean temperature, HR, IBI and EDA tonic values of the next day were predicted with root mean square error (RMSE) of 0.13 ± 0.07 (C°), 1.31 ± 0.34 (bpm), 0.016 ± 0.005 (s) and 0.17 ± 0.17 (μS), respectively.