  The temporal analysis of stellar activity evolution is usually dominated by a
complex trade-off between model complexity and interpretability, often by
neglecting the non-stationary nature of the process. Recent studies appear to
indicate that the presence of multiple coexisting cycles in a single star is
more common than previously thought. The correct identification of physically
meaningful cyclic components in spectroscopic time series is therefore a
crucial task, which cannot overlook local behaviors. Here we propose a
decomposition technique which adaptively recovers amplitude- and
frequency-varying components. We present our results for the solar activity as
measured both by the sunspot number and the $K$-line emission index, and we
consistently recover the Schwabe and Gleissberg cycles as well as the
Gnevyshev-Ohl pattern probably related to the Hale cycle. We also recover the
known 8-year cycle for 61 Cygni A, in addition to evidence of a three-cycles
long pattern reminiscent of the Gnevyshev-Ohl rule. This is particularly
interesting as we cannot discard the possibility of a relationship between the
measured field polarity reversals and this Hale-like periodicity.
