The dynamic Allan Variance III: Confidence and detection surfaces

The dynamic Allan variance (DAVAR) is a surface which describes the stability of a high-precision clock with respect to time. When the DAVAR is evaluated from experimental data, its surface shows random fluctuations caused by the estimation process. It is fundamental to assign a statistical significance to these fluctuations, so that they can be differentiated from the variations of the surface caused by clock anomalies. First, we develop confidence surfaces to assign a statistical significance to the random fluctuations of the DAVAR estimator. Then, we introduce detection surfaces to reveal the variations of the surface caused by clock anomalies. We validate the obtained results through numerical simulations.