New Insights into Time Series Analysis IV: Panchromatic and Flux Independent Period Finding Methods.

New time-series analysis tools are needed in disciplines as diverse as astronomy, economics and meteorology. In particular, the increasing rate of data collection at multiple wavelengths requires new approaches able to handle these data. The panchromatic correlated indices $K^{(s)}_{(fi)}$ and $L^{(s)}_{(pfc)}$ are adapted to quantify the smoothness of a phased light-curve resulting in new period-finding methods applicable to single- and multi-band data. Simulations and observational data are used to test our approach. The results were used to establish an analytical equation for the amplitude of the noise in the periodogram for different false alarm probability values, to determine the dependency on the signal-to-noise ratio, and to calculate the yield-rate for the different methods. The proposed method has similar efficiency to that found for the String Length period method. The effectiveness of the panchromatic and flux independent period finding methods in single waveband as well as multiple-wavebands that share a fundamental frequency is also demonstrated in real and simulated data.