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2018 Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity
Jean-Marc Bardet, Paul Doukhan
Electron. J. Statist. 12(2): 2323-2354 (2018). DOI: 10.1214/18-EJS1459

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 $X_{t}=a_{t}(t/nT)X_{t-1}+\xi_{t}$ for $t\in \mathbb{N}$ and with $a_{t+T}\equiv a_{t}$. Central limit theorems are established for kernel estimators $\widehat{a}_{s}(u)$ reaching classical minimax rates and only requiring low order moment conditions of the white noise $(\xi_{t})_{t}$ up to the second order.

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Jean-Marc Bardet. Paul Doukhan. "Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity." Electron. J. Statist. 12 (2) 2323 - 2354, 2018. https://doi.org/10.1214/18-EJS1459

Information

Received: 1 February 2018; Published: 2018
First available in Project Euclid: 25 July 2018

zbMATH: 06917478
MathSciNet: MR3832094
Digital Object Identifier: 10.1214/18-EJS1459

Subjects:
Primary: 62G05, 62M10
Secondary: 60F05

JOURNAL ARTICLE
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Vol.12 • No. 2 • 2018
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