TY  - GEN
ID  - heidok12041
A1  - Paraschakis, Konstantinos
Y1  - 2011///
N2  - A classical model in time series analysis is a stationary process superposed by one or several deterministic sinusoidal components. Di erent methods are applied to estimate the frequency (w) of those components such as Least Squares Estimation and the maximization of the periodogram. In many applications the assumption of a constant frequency is violated and we turn to a time dependent frequency function (w(s)). For example in the physics literature this is viewed as nonlinearity of the phase of a process. A way to estimate w(s) is the local application of the above methods. In this dissertation we study the maximum periodogram method on data segments as an estimator of w(s) and subsequently a least squares technique for estimating the phase. We prove consistency and asymptotic normality in the context of "infill asymptotics", a concept that off ers a meaningful asymptotic theory in cases of local estimations. Finally, we investigate an estimator based on a local linear approximation of the frequency function, prove its consistency and asymptotic normality in the "infi ll asymptotics" sense and show that it delivers better estimations than the ordinary periodogram. The theoretical results are also supported by some simulations.
TI  - Frequency and phase estimation in time series with quasi periodic components
AV  - public
UR  - https://archiv.ub.uni-heidelberg.de/volltextserver/12041/
KW  - Periodogram 
KW  -  Frequency estimation 
KW  -  Phase estimation 
KW  -  Time Series 
KW  -  Nonstationary
ER  -