ALLAN VARIANCE AND THE UNCERTAINTY OF AUTOCORRELATED MEASUREMENTS

In metrology, the uncertainty of the mean of repeated measurements is often calculated by the sample standard deviation of the measurements divided by the square root of the sample size. When the measurements are autocorrelated, in particular when they are from a stationary process, a recent paper in Metrologia (Zhang 2006) provided all approach to calculate the corresponding uncertainty. However, when the measurements are from a nonstationary process, how to assess their uncertainty remains unresolved. Allan variance or two-sample variance has been used for more than three decades as a substitute for the classical variance to characterize the stability of clocks or frequency standards when the underlying process is a 1/f noise process. Recently, from the point of view of the time domain, a paper in Metrologia (Zhang, 2008) studied the Allan variance and its properties for stationary processes, random walk, and long-memory processes such as the fractional difference processes This paper discusses the use of Allan variance as all alternative measure of uncertainty for measurements from time series models. The results show that the Allan variance is a better measure of the process variation than the classical variance of the random walk and the nonstationary fractional difference processes including the 1/f noise.