Detecting Periodicity of a General Stationary Time Series via AR(2)-Model Fitting
Fuente:
arXiv
Salvato in:
| Autori principali: | , , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2025
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866918222173831168 |
|---|---|
| author | Kreiss, Jens-Peter Maouris, Panagiotis Paparoditis, Efstathios |
| author_facet | Kreiss, Jens-Peter Maouris, Panagiotis Paparoditis, Efstathios |
| contents | 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 a general stationary processes possessing a spectral density with a dominant peak at some frequency $λ_0\in(0,π)$. 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 $λ_0$. To investigate consistency properties of the AR(2) based estimator of $λ_0$, 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 $λ_0$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2511_23094 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Detecting Periodicity of a General Stationary Time Series via AR(2)-Model Fitting Kreiss, Jens-Peter Maouris, Panagiotis Paparoditis, Efstathios Statistics Theory 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 a general stationary processes possessing a spectral density with a dominant peak at some frequency $λ_0\in(0,π)$. 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 $λ_0$. To investigate consistency properties of the AR(2) based estimator of $λ_0$, 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 $λ_0$ 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. |
| title | Detecting Periodicity of a General Stationary Time Series via AR(2)-Model Fitting |
| topic | Statistics Theory |
| url | https://arxiv.org/abs/2511.23094 |