Frequency and phase estimation in time series with quasi periodic components


Konstantinos Paraschakis, Institut für Angelwandte Mathematic, Universtät Heidelberg, Im Neuenheimer Feld 294, 69120 Heidelberg, Germany.


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.