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Frequency and phase estimation in time series with quasi periodic components
Author(s) -
Paraschakis Konstantinos,
Dahlhaus Rainer
Publication year - 2012
Publication title -
journal of time series analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.576
H-Index - 54
eISSN - 1467-9892
pISSN - 0143-9782
DOI - 10.1111/j.1467-9892.2011.00736.x
Subject(s) - mathematics , series (stratigraphy) , asymptotic distribution , constant (computer programming) , consistency (knowledge bases) , phase (matter) , strong consistency , estimator , least squares function approximation , hilbert transform , statistics , spectral density , computer science , discrete mathematics , programming language , paleontology , chemistry , organic chemistry , biology
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.