Estimating the Modified Allan Variance

A paper at the 1992 FCS showed how to express the modified Allan variance (mvar) in terms of the third difference of the cumulative sum of time residuals. Although this reformulated definition was presented merely as a computational trick for simplifying the calculation of mvar estimates, it has since turned out to be a powerful theoretical tool for deriving the statistical quality of those estimates in terms of their equivalent degrees of freedom (edf), defined for an estimator V by edf V = 2(EV)2/(var V). Confidence intervals for mvar can then be constructed from levels of the appropriate 2 distribution.