Several publications have published results indicating that breathing rate is higher in mid-luteal phase compared to the mid-follicular phase.

An increased breathing rate can be an indicator that ovulation took place.

Tenan, M.S., Brothers, R.M., Tweedell, A.J., Hackney, A.C., & Griffin, L. (2014). Changes in resting heart rate variability across the menstrual cycle. Psychophysiology, 51, 996-1004.

de Zambotti, Nicholas, Colrain, Trinder, & Baker. (2013). Autonomic regulation across phases of the menstrual cycle and sleep stages in women.

Little, B. C., & Zahn, T. P. (1974). Changes in mood and autonomic functioning during the menstrual cycle. Psychophys, 11(5): 579-590.