1. It contrasts with the autocorrelation function , which does not control for other lags. 2. The autocorrelation function is a statistic defined as 3. This autocorrelation function has a peak at the origin, where the original source was. 4. Thus { x _ n } cannot be distinguished from white noise using the autocorrelation function . 5. Given the time series x [ t ], its non-stationary autocorrelation function is given by 6. Let the aperiodic autocorrelation function of the sequence "'x "'be defined by 7. These algorithms derive from the exact theoretical relation between the partial autocorrelation function and the autocorrelation function. 8. These algorithms derive from the exact theoretical relation between the partial autocorrelation function and the autocorrelation function . 9. Here, \ ddot ( 0 ) is the second derivative of the autocorrelation function evaluated at zero. 10. The Siegert equation relates the second-order autocorrelation function with the first-order autocorrelation function as follows:
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