The sample autocorrelation function and the detection of long-memory processes

► Long memory cannot be indicated using the sum of the usually defined sample autocorrelations. ► The sample spectral density is zero evaluated at the zero frequency. ► Whatever the pattern of the theoretical autocorrelations, there must be at least one negative ρˆ(h). ► The sum of the third order sample (auto) bicorrelations at lags h,k≥1, equals 1/3. ► Routine calculation of the sums of the sample autocorrelations or bicorrelations is inadvisable.