Simulation output analysis using integrated paths

This article considers the steady-state simulation output analysis problem for a process that satisfies a functional central limit theorem. We construct an estimator for the time-average variance constant that is based on iterated integrations of the sample path. When the observations are batched, the method generalizes the method of batch means. One advantage of the method is that it can be used without batching the observations; that is, it can allow for the process variance to be estimated at any time as the simulation runs without waiting for a fixed time horizon to complete. When used in conjunction with batching, the method can improve efficiency (the reciprocal of work times mean-squared error) compared with the standard method of batch means. In numerical experiments, efficiency improvement ranged from a factor of 1.5 (for the waiting time sequence in an M/M/1 queueing system with a single integrated path) up to a factor of 14 (for an autoregressive process and 19 integrated paths).