The Bayesian statistical methods of Gregory–Loredo and the Bretthorst generalization of the Lomb–Scargle periodogram are used to study the activity cycles of the early K-type subgiant star CF Oct. We use a ∼45-yr-long data set derived from archival photographic observations, published photoelectric photometry, the Hipparcos data series and the All Sky Automated Survey archive. We confirm the already known rotational period for the star of 20.16 d and provide evidence that it has exhibited changes from 19.90 to 20.45 d. This is an indication of stellar surface differential rotation. The Bayesian magnitude and time-residual analysis clearly reveals at least one long-term cycle. The posterior distributions of the cycle length appear to be multimodal with pronounced peaks at a period of 7.1 yr with a full width at half-maximum (FWHM) of 54 d for time-residuals and at a period of 9.8 yr with a FWHM of 184 d for magnitude data. These results are consistent with the previously postulated cycle of 9 ± 3 yr.