Moving least squares spectra scrutinize chronomics in and around us

As an extension of the chronobiological serial section, gliding spectra illustrate the changing time structure (chronome) of physiological, physical and/or other variables in a given frequency range. For this purpose, least squares spectra are computed over a specified interval (much shorter than the observation span) that is progressively displaced by a given increment throughout the entire record. Results can be displayed either as 3D charts or as surface charts, displaying the estimated amplitudes, percentage rhythms or ordering P-values at each trial period for each interval. The procedure is illustrated for the record of Wolf numbers as a gauge of solar activity and for the number of marriages and divorces in Japan during the past century. Major components in these time series show deviations in period length and relative prominence over time. Particularly in the case of non-stationary time series, gliding spectra offer themselves as useful tools to examine changes in time structure beyond a specific spectral component.