On multiwindow estimators for correlation

We have examined the bias and variance properties of a recently suggested class of multiwindow estimators for autocorrelation functions (ACF). The derived exact expression for the bias is valid for any amplitude distribution, while the derived exact result for the variance is valid for zero-mean Gaussian processes. We show that the multiwindow ACF estimator has undesirable bias properties and inferior variance properties compared to the standard ACF estimator. The reason is that the correlation properties of the windows contribute directly to the ACF estimator and its statistical moments. The lesson to be learned is that what is good for spectral estimators is not necessarily good for correlation estimators