Electronic Journal of Statistics

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

Jean-Marc Bardet and Paul Doukhan

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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.

Article information

Electron. J. Statist., Volume 12, Number 2 (2018), 2323-2354.

Received: February 2018
First available in Project Euclid: 25 July 2018

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Digital Object Identifier

Primary: 62G05: Estimation 62M10: Time series, auto-correlation, regression, etc. [See also 91B84]
Secondary: 60F05: Central limit and other weak theorems

Local stationarity nonparametric estimation central limit theorem

Creative Commons Attribution 4.0 International License.


Bardet, Jean-Marc; Doukhan, Paul. Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity. Electron. J. Statist. 12 (2018), no. 2, 2323--2354. doi:10.1214/18-EJS1459. https://projecteuclid.org/euclid.ejs/1532484332

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