Multivariate autoregressive techniques for constructing confidence regions on the mean vector

The authors develop a method for constructing confidence regions on the mean vectors of multi-variate processes that is based on a vector autoregressive (VAR) representation of the data-generating process. A confidence-region-construction algorithm for a general autoregressive model is given. The authors establish the asymptotic validity of the confidence-region estimator (that is, the exact achievement of nominal coverage probability as the sample size tends to infinity) when the output process is a stationary vector autoregressive process of known, finite order. With respect to confidence-region volume, coverage probability, and execution time, they carry out an experimental performance comparison of VAR versus the methods of Bonferroni Batch Means (BBM), Multivariate Batch Means (MBM), and Multivariate Spectral Analysis (SPA). The experimental results indicate that (i) VAR delivered confidence regions with the smallest volume; (ii) BBM delivered confidence regions with the largest volume, the highest coverage and the smallest execution time; (iii) in small samples, all of the methods might yield confidence-region estimators whose coverage differs significantly from the nominal level; and (iv) in large samples for which the sample autocorrelation function indicates a vector autoregressive dependence structure, VAR is a viable technique for simulation output analysis.