Modified Confidence Intervals for the Mean of an Autoregressive Process

摘要

The author's motivation is to find asymptotically more accurate confidence intervals for the steady state mean of a simulated process. By this he means that the coverage probability error for the confidence intervals we derive should be of lower order than that of standard confidence intervals. There are several standard methods of setting confidence intervals in simulations, including the regenerative method, batch means, and time series methods. He focuses on improved confidence intervals for the mean of an autoregressive process, and as such our results are useful outside of a simulation setting. Additional keywords: time series analysis; Cornish-Fisher expansions; Edgeworth expansions.