A technique for generating confidence intervals on the common expectation of a sequence of correlated random variables is developed. The sequence is modelled as a covariance stationary process. In this situation the variance of the sample mean is proportional to the variance spectrum at zero frequency. This value of the spectrum is estimated by fitting a low order polynomial to the sample spectrum (periodogram) in the lower frequency region. The technique is applicable to both individual observations and batched data. Experimental results comparing it with the method of batch means are given for the steady state waiting time of the M/M/1 queue. The proposed technique gives valid confidence intervals of approximately the same average width as the method of batch means when the batch size is large enough for that method to be valid. It continues to give valid confidence intervals when the batch sizes are such that the method of batch means breaks down.