A note on the sum of the sample autocorrelation function

It is shown that the sum of the sample autocorrelation function at lag h≥1h≥1 is always −12 for any stationary time series with arbitrary length T≥2T≥2 (Hassani, 2009 [1]). In this paper, the distribution of a set of the sample autocorrelation function using the properties of this quantity is considered. It is found that the distribution of a set of the sample autocorrelation estimates is not independent and identically distributed. This finding implies that the result of diagnostic check and model building using the traditional assumption of iid can be quite misleading.