Atomic clock models using fractionally integrated noise processes

The existence of power-law noise structures in the measurements of atomic clocks has been well documented in the literature. Each of these power-law noises exhibits a spectral density proportional to 1/f^α at low frequencies. There is, however, another class of noise, termed fractionally integrated or long-memory noise, which too possesses spectral densities of this form. These fractionally integrated noises are analysed and applied to atomic timescales in this research. An alternative atomic clock model is developed and validated via simulation and live data tests. Estimators of clock rate and drift which account for the long-memory noise structures are derived and shown to produce both superior estimates of rate and drift and superior reports of the variability of these estimates. Estimation strategies which account for the autocovariance structures characteristic of fractionally integrated noise are also found to yield more powerful tests of hypotheses than do the short-memory techniques historically employed.