time or normalized frequency samples in blocks of n samples prior to processing. The resulting predictor becomes or for the time series: The overlapping estimators have far superior performance over the non-overlapping estimators, as n rises and the time-series is of moderate length. The overlapped estimators have been accepted as the preferred Allan variance estimators in IEEE, ITU-T and ETSI standards for comparable measurements such as needed for telecommunication qualification. Modified Allan variance In order to address the inability to separate white phase modulation from flicker phase modulation using traditional Allan variance estimators, an algorithmic filtering reduces the bandwidth by n. This filtering provides a modification to the definition and estimators and it now identifies as a separate class of variance called modified Allan variance. The modified Allan variance measure is a frequency stability measure, just as is the Allan variance. Time stability estimators A time stability (σx) statistical measure, which is often called the time deviation (TDEV), can be calculated from the modified Allan deviation (MDEV). The TDEV is based on the MDEV instead of the original Allan deviation, because the MDEV can discriminate between white and flicker phase modulation (PM). The following is the time variance estimation based on the modified Allan variance: and similarly for modified Allan deviation to time deviation: The TDEV is normalized so that it is equal to the classical deviation for white PM for time constant τ = τ0. To understand the normalization scale factor between the statistical measures, the following is the relevant statistical rule: For independent random variables X and Y, the variance (σz2) of a sum or difference (z = x − y) is the sum square of their variances (σz2 = σx2 + σy2). The variance of the sum or difference (y = x2τ − xτ) of two independent samples of a random variable is twice the variance of the random variable (σy2 = 2σx2). The MDEV is the second difference of independent phase measurements (x) that have a variance (σx2). Since the calculation is the double difference, which requires three independent phase measurements (x2τ − 2xτ + x), the modified Allan variance (MVAR) is three times the variances of the phase measurements. Other estimators Further developments have produced improved estimation methods for the same stability measure, the variance/deviation of frequency, but these are known by separate names such as the Hadamard variance, modified Hadamard variance, the total variance,