  We formulate an improved time series analysis method for the analysis of
photometry of active stars. This new Continuous Period Search (CPS) method is
applied to 12 years of V band photometry of the young solar analogue HD 116956
(NQ UMa). The new method is developed from the previous Three Stage Period
Analysis (TSPA) method. Our improvements are the use of a sliding window in
choosing the modelled datasets, a criterion applied to select the best model
for each dataset and the computation of the time scale of change of the light
curve. We test the performance of CPS with simulated and real data. The CPS has
a much improved time resolution which allows us to better investigate fast
evolution of stellar light curves. We can also separate between the cases when
the data is best described by periodic and aperiodic (e.g. constant brightness)
models. We find, however, that the performance of the CPS has certain
limitations. It does not determine the correct model complexity in all cases,
especially when the underlying light curve is constant and the number of
observations too small. Also the sensitivity in detecting two close light curve
minima is limited and it has a certain amount of intrinsic instability in its
period estimation. Using the CPS, we find persistent active longitudes in the
star HD 116956 and a "flip-flop" event that occurred during the year 1999.
Assuming that the surface differential rotation of the star causes observable
period variations in the stellar light curve, we determine the differential
rotation coefficient to be |k|>0.11. The mean timescale of change of the light
curve during the whole 12 year observing period was T_C=44.1 d, which is of the
same order as the predicted convective turnover time of the star. We also
investigate the presence of activity cycles on the star, but do not find any
conclusive evidence supporting them.
