Simulated trends in pulsation period (top panel) combined with a constant amplitude (bottom panel) as estimated by the localkernel method. Thin red, green and blue solid lines in the top panel: the simulated values using slopes 0, 0.25 and 1 times that of OGLE-LMC-CEP-1405 (such that the blue line coincides with the trend component found for this Cepheid). The true amplitude, which had the same constant value in all simulations, is represented by a blue line in the bottom panel. Dotted red, green and blue lines: the pointwise median of the kernel estimates on the 250 repetitions. The colors show a 95% symmetric confidence band around the median.