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Conference Agenda

Overview and details of the sessions of this conference. Please select a date or location to show only sessions at that day or location. Please select a single session for detailed view (with abstracts and downloads if available).

Daily Overview

Session

Nonparametric statistics
Location: 0.004
Session Chair: Anne Leucht

Presentation 2

Detecting Periodicity of a General Stationary Time Series via AR(2)-Model Fitting

Jens-Peter Kreiss¹, Panagiotis Maouris², Efstathios Paparoditis³

1: TU Braunschweig, Germany; 2: University of Cyprus; 3: Cyprus Academy of Sciences, Letters and Arts

Estimating the periodicity of a stationary time series via fitting a second order stationary autoregressive (AR(2)) model has been initiated by the seminal paper of Yule(1927). We investigate properties of this procedure when applied to general stationary processes possessing a spectral density with a dominant peak at some frequency λ₀in (0,π).
We show that if the peak of the spectral density is sharp enough (in a way to be specified) then the AR(2) model, which best (in mean square sense) approximates the underlying process, correctly identifies the frequency λ₀.
To investigate consistency properties of the AR(2) based estimator of λ₀, a near to pole framework is adopted. Triangular arrays of stationary stochastic processes are considered that possess a spectral density the peak of which at λ₀ becomes more pronounced as the sample size n of the observed time series increases to infinity. It is shown in this set up, that the AR(2) based estimator achieves a rate of convergence which is larger than the parametric n^-1/2-rate and which can be arbitrarily close to n^-2/3, the best rate that can be achieved by this estimator.