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arXiv · 1705.10140

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

Jean-Marc Bardet·Paul Doukhan
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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)X t--1 + $\xi$t for t $\in$ N and with a t+T $\not\equiv$ at. Central limit theorems are established for kernel estima-tors as(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. 2017-05-29. Non-parametric estimation of time varying AR(1)--processes with local stationarity and periodicity. https://arxiv.org/abs/1705.10140

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