  We develop a new smoothing or extrapolating method, based on discrete
Laguerre functions, for systematically analyzing the stochastic signal of
shifted-contour auxiliary-field Monte Carlo. We study the statistical errors
and extrapolation errors using full configuration-interaction energies for the
doubly stretched water molecule. The only free parameter is the order N of the
fit. We show that low N emphasizes stability while higher N enable improved
extrapolation, at the cost of increased statistical errors. Typically, one
should use low order for signals based on a small number of iterations while
higher order is efficacious for signals based on large number of iterations. We
provide a heuristic algorithm for determining the order to be used and show its
utility.
