Using Modified Allan Variance for Time Series Analysis

Allan Variance (AVAR) was introduced more than 40 years ago as an estimator of the stability of frequency standards. Now it is also used for investigations of time series in astronomy and geodesy. However, there are several issues with this method that need special consideration. First, unlike frequency measurements, astronomical and geodetic time series usually consist of data points with unequal uncertainties. Thus one needs to apply data weighting during statistical analysis. Second, some sets of scalar time series naturally form multidimensional vector series. For example, Cartesian station coordinates form the 3D station position vector. The original AVAR definition does not allow one to process unevenly weighted and/or multidimensional data. To overcome these deficiencies, AVAR modifications were proposed in Malkin (2008. On the accuracy assessment of celestial reference frame realizations. J Geodesy 82: 325-329). In this paper, we give some examples of processing geodetic and astrometric time series using the classical and the modified AVAR approaches, and compare the results.