Smoothing and extrapolating shifted-contour auxiliary-field Monte Carlo signals using discrete Laguerre functions

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.