  Women's basal body temperature (BBT) follows a periodic pattern that is
associated with the events in their menstrual cycle. Although daily BBT time
series contain potentially useful information for estimating the underlying
menstrual phase and for predicting the length of current menstrual cycle, few
models have been constructed for BBT time series. Here, we propose a
state-space model that includes menstrual phase as a latent state variable to
explain fluctuations in BBT and menstrual cycle length. Conditional
distributions for the menstrual phase were obtained by using sequential
Bayesian filtering techniques. A predictive distribution for the upcoming onset
of menstruation was then derived based on the conditional distributions and the
model, leading to a novel statistical framework that provided a sequentially
updated prediction of the day of onset of menstruation. We applied this
framework to a real dataset comprising women's self-reported BBT and days of
menstruation, comparing the prediction accuracy of our proposed method with
that of conventional calendar calculation. We found that our proposed method
provided a better prediction of the day of onset of menstruation. Potential
extensions of this framework may provide the basis of modeling and predicting
other events that are associated with the menstrual cycle.

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