Properties of Batch Means from Stationary ARMA (Autoregressive Moving Average) Time Series

摘要

The batch means process arising from an arbitrary autoregressive moving-average (ARMA) process time series is derived. As side results, the variance and correlation structures of the batch means process as functions of the batch size and parameters of the original process are obtained. Except for the first-order ARMA process, for which a closed-form expression is obtained, the parameters of the batch-means process are determined numerically. Keywords: Monte Carlo method; Simulation. (Author)