The Allan Variance as an Estimator of the Long-memory Parameter: Time-domain and Wavelet Methods

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