  This paper contributes to the field of modeling and hindcasting of the total
solar irradiance (TSI) based on different proxy data that extend further back
in time than the TSI that is measured from satellites.
  We introduce a simple method to analyze persistent frequency-dependent
correlations (FDCs) between the time series and use these correlations to
hindcast missing historical TSI values. We try to avoid arbitrary choices of
the free parameters of the model by computing them using an optimization
procedure. The method can be regarded as a general tool for pairs of data sets,
where correlating and anticorrelating components can be separated into
non-overlapping regions in frequency domain.
  Our method is based on low-pass and band-pass filtering with a Gaussian
transfer function combined with de-trending and computation of envelope curves.
  We find a major controversy between the historical proxies and
satellite-measured targets: a large variance is detected between the
low-frequency parts of targets, while the low-frequency proxy behavior of
different measurement series is consistent with high precision. We also show
that even though the rotational signal is not strongly manifested in the
targets and proxies, it becomes clearly visible in FDC spectrum.
  The application of the new method to solar data allows us to obtain important
insights into the different TSI modeling procedures and their capabilities for
hindcasting based on the directly observed time intervals.

Solar and Stellar Astrophysics;Data Analysis, Statistics and Probability;Geophysics