Context : Aims : 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 ) . Methods : 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 . Results : 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 ( i.e . rotational modulation of brightness ) 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 \overline { 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 . Conclusions :