Allan Variance and the Uncertainty of the Autocorrelated Measurements

When repeated measurements are autocorrelated, it is not appropriate to use the traditional approach to calculate the uncertainty of the average of the measurements, which assumes that the measurements are statistically independent. In Zhang (2006), a practical approach to calculate the corresponding uncertainty and the confidence interval when the data are from a stationary process was proposed. However, when the data are from a non-stationary process such as a random walk or a 1/f noise, the classical variance is inappropriate to characterize the process. Allan variance has been used to characterize the stability of clock or frequency standards and recently the noise of Zener-diode voltage standards. However, it has been used mostly for its properties related to the power spectrum density for a variety of stochastic process, in particular, the 1/f noise. In this paper, we study the property of the Allan variance for various time series in the time domain and demonstrate that it is alternative measure for some autocorrelated data in assessing the uncertainty.

Dr. Nien-Fan Zhang
Statistical Engineering Division
NIST