Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity

Jean Marc Bardet; Paul Doukhan

doi:10.1214/18-EJS1459

Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity

Jean Marc Bardet
, Paul Doukhan

Université Panthéon-Sorbonne (Paris 1)
University Cergy-Pontoise
CIMFAV

Résultats de recherche: Contribution à un journal › Article › Revue par des pairs

8 Citations (Scopus)

Résumé

Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (X_t), with local stationarity and periodic features (with a known period T), inducing the definition X_t = a_t(t/nT)X_t−1 + ξt for t ∈ N and with a_t+T ≡ a_t. Central limit theorems are established for kernel estimators â_s(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξ_t)_t up to the second order. MSC 2010 subject classifications: Primary 62G05, 62M10; secondary60F05.

langue originale	Anglais
Pages (de - à)	2323-2354
Nombre de pages	32
journal	Electronic Journal of Statistics
Volume	12
Numéro de publication	2
Les DOIs	https://doi.org/10.1214/18-EJS1459
état	Publié - 1 janv. 2018
Modification externe	Oui

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title = "Non-parametric estimation of time varying AR(1){\textendash}processes with local stationarity and periodicity",

abstract = "Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)Xt−1 + ξt for t ∈ N and with at+T ≡ at. Central limit theorems are established for kernel estimators {\^a}s(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξt)t up to the second order. MSC 2010 subject classifications: Primary 62G05, 62M10; secondary60F05.",

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N2 - Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)Xt−1 + ξt for t ∈ N and with at+T ≡ at. Central limit theorems are established for kernel estimators âs(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξt)t up to the second order. MSC 2010 subject classifications: Primary 62G05, 62M10; secondary60F05.

AB - Extending the ideas of [7], this paper aims at providing a kernel based non-parametric estimation of a new class of time varying AR(1) processes (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)Xt−1 + ξt for t ∈ N and with at+T ≡ at. Central limit theorems are established for kernel estimators âs(u) reaching classical minimax rates and only requiring low order moment conditions of the white noise (ξt)t up to the second order. MSC 2010 subject classifications: Primary 62G05, 62M10; secondary60F05.

KW - Central limit theorem

KW - Local stationarity

KW - Nonparametric estimation

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JO - Electronic Journal of Statistics

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IS - 2

ER -

Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity

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