THE ALLAN VARIANCE AS AN ESTIMATOROF THE LONG-MEMORY PARAMETER:TIME-DOMAIN AND WAVELET METHODS

摘要

The Allan variance is a well-known estimator of frequency stability and is often used tornclassify a time series into one of the standard clock noise types. By identifying the power-lawrnmodel for clock noise with its long-memory equivalent, the Allan variance can also serve as anrnestimate for the long-memory parameter. Although the Allan variance is not a maximumrnlikelihood estimator, it can be used with regression techniques that employ minimum variancernestimates. This work describes the analytic basis for using the Allan variance to estimate thernmemory parameter, and performance of several Allan-variance-based estimators is illustratedrnvia simulation study. Maximum likelihood estimation is also discussed, and the performance ofrnmaximum-likelihood estimators is contrasted with that of the Allan-variance-based estimators.