We derive the bias, variance, covariance, and mean square error of the
standard lag windowed correlogram estimator both with and without sample mean
removal for complex white noise with an arbitrary mean. We find that the
arbitrary mean introduces lag dependent covariance between different lags of
the correlogram estimates in spite of the lack of covariance in white noise for
non-zeros lags. We provide a heuristic rule for when the sample mean should be,
and when it should not be, removed if the true mean is not known. The sampling
properties derived here are useful is assesing the general statistical
performance of autocovariance and autocorrelation estimators in different
parameter regimes. Alternatively, the sampling properties could be used as
bounds on the detection of a weak signal in general white noise.Comment: 11 pages, 2 figures, To be published in Journal of Time Series
Analysi
