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

Research output: Contribution to journal › Article › peer-review

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 (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.

Original language	English
Pages (from-to)	2323-2354
Number of pages	32
Journal	Electronic Journal of Statistics
Volume	12
Issue number	2
DOIs	https://doi.org/10.1214/18-EJS1459
Publication status	Published - 1 Jan 2018
Externally published	Yes

Keywords

Central limit theorem
Local stationarity
Nonparametric estimation

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10.1214/18-EJS1459

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title = "Non-parametric estimation of time varying AR(1)–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.",

keywords = "Central limit theorem, Local stationarity, Nonparametric estimation",

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T1 - Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity

AU - Bardet, Jean Marc

AU - Doukhan, Paul

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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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EP - 2354

JO - Electronic Journal of Statistics

JF - Electronic Journal of Statistics

IS - 2

ER -

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

Abstract

Keywords

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