It is around a century that sample autocorrelation function (ACF) has been introduced and used as a standard tools in time series analysis. A vast literature can be found on the statistical properties of the sample ACF. It has been shown that the sum of the sample autocorrelation over the lags 1 to T − 1 is - 0.5 for all time series of length T ([1]-[5]). However, this property has not been deeply discussed in the literature. To the researchers and students it must appear mysterious that standard textbooks on time series analysis fail to acknowledge this property. This paper, consider this property and try to follow up the drawback that might be seen with the application of sample ACF in practice.
