Methods of Reverberation Mapping. I. Time-lag Determination by Measures
  of Randomness
  A class of methods for measuring time delays between astronomical time series
is introduced in the context of quasar reverberation mapping, which is based on
measures of randomness or complexity of the data. Several distinct statistical
estimators are considered that do not rely on polynomial interpolations of the
light curves nor on their stochastic modeling, and do not require binning in
correlation space. Methods based on von Neumann's mean-square
successive-difference estimator are found to be superior to those using other
estimators. An optimized von Neumann scheme is formulated, which better handles
sparsely sampled data and outperforms current implementations of discrete
correlation function methods. This scheme is applied to existing reverberation
data of varying quality, and consistency with previously reported time delays
is found. In particular, the size-luminosity relation of the broad-line region
in quasars is recovered with a scatter comparable to that obtained by other
works, yet with fewer assumptions made concerning the process underlying the
variability. The proposed method for time-lag determination is particularly
relevant for irregularly sampled time series, and in cases where the process
underlying the variability cannot be adequately modeled.
