In stereo matching of images, sample cross-covariances are used commonly as a criterion for deciding whether matched points are truly conjugate. Hereupon window width is a serious parameters to dominate matching stability. This paper argues about relation of matching stability with window width in terms of statistical behavior of sample covariances. For simple circumstances of analysis auto-covariances of a single image are considered instead of cross-covariances of stereo ones. First the mean and variance of sample auto-covariances are derived with parameters, window width and positional lag. Secondly they are evaluated from the correlation function estimated on an aerial image under the assumption of ergodicity to observe how they vary according as two parameters vary. From this result a variation factor is proved usefull to estimate appropriate window width.