Frequency and phase estimation in time series with quasi periodic components

In this article, we consider frequency and phase estimation in a noisy oscillation with potentially non-constant phase increments resulting from an underlying non-constant frequency. A maximum periodogram method on segments is used to estimate the time-varying frequency and a subsequent least squares approach to estimate the phase. A key problem addressed in this article is the question how to set up a meaningful concept of asymptotic statistics for this model. This problem is solved by a special infill asymptotics concept. We use this concept to prove consistency and asymptotic normality of the estimates. Furthermore, the phase estimate is compared to the Hilbert transform in a simulation.