Autoregressive analysis, in conjunction with component selection heuristics and least-squares refinement, here called ARM+LSQ, leads to parameterizations that are optimal in the following sense. Empirical Monte Carlo investigation of simulated data sets shows that using fewer components than determined by the heuristics ignores some information in the data since the parameterizations cannot fit the data within the noise. Using larger numbers of components than suggested by the heuristics leads to multiple local minima, or wide parameter ranges, all giving comparable agreement with the data. Similarly, the Cramér-Rao uncertainty bound shows that the parameters overlap extensively when too many components are considered. Physical meaning can be ascribed to the resulting parameters as follows. A relaxation component represents an underlying distribution of components whose width is no larger than the resolution of the experiment. That distribution may be sharp or broad up to the resolution limit, and it is not possible to distinguish these possibilities from the ARM+LSQ parameterization or any other method without additional knowledge or assumptions.