Allan Variance

The Allan variance is a measure of the stability of a time series of fractional-frequency deviations from a frequency source. Divide the time series into consecutive, nonoverlapping intervals of duration , and let be the arithmetic mean over the th interval. The Allan variance at averaging time is

Here the angle brackets denote averaging over . The square root is the Allan deviation. Unlike the ordinary variance, the Allan variance is formed from first differences of adjacent block arithmetic means and can remain useful for some nonstationary noise models.