Properties of Batch Means from Stationary ARMA (1, 1) Time Series.

For stationary first order autoregressive and autoregressive moving average processes with normally distributed errors, the corresponding stationary process of batch means is shown to be an autoregressive moving average process. The batch means process resulting from a moving average process, however, is shown to be a moving average process. The parameters of the batch means process are closed form functions of the batch size and parameters of the original process.