We derive the second-order sampling properties of certain autocovariance and
autocorrelation estimators for sequences of independent and identically
distributed samples. Specifically, the estimators we consider are the classic
lag windowed correlogram, the correlogram with subtracted sample mean, and the
fixed-length summation correlogram. For each correlogram we derive explicit
formulas for the bias, covariance, mean square error and consistency for
generalised higher-order white noise sequences. In particular, this class of
sequences may have non-zero means, be complexed valued and also includes
non-analytical noise signals. We find that these commonly used correlograms
exhibit lag dependent covariance despite the fact that these processes are
white and hence by definition do not depend on lag.Comment: Submitted to Biometrik
