Adaptive Spectral Methods for Simulation Output Analysis

This paper addresses two central problems in simulation methodology: the generation of conjidence intervals for the steady state means of the output sequences and the sequential use of these conjidence intervals to control the run length. The variance of the sample mean of a covariance stationary process is given approximately by p(O)lN, where p( f ) is the spectral density at frequency f and N is the sample size. In an e rlier paper we developed a method of confidence interval generation based on the estimation of p(0) through the least squares jit of a quadratic to the logarithm of the periodogram. This method was applied in a run length Control procedure to a sequence of batched means. As the run length increased the batch means were rebatched into larger batch sizes so as to limit storage requirements. In this rebatching the shape of the spectral density changes, gradually becoming flat as N increases. Quadratics were chosen as a compromise between small sample bias and large sample stability.