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Pré-Publication, Document De Travail Année : 2017

Lag ACF Series X

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

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 (Xt), with local stationarity and periodic features (with a known period T), inducing the definition Xt = at(t/nT)X t−1 + ξt for t ∈ N and with a t+T ≡ 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 (ξt)t up to the second order.
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Dates et versions

hal-01527749 , version 1 (27-05-2017)
hal-01527749 , version 2 (20-07-2018)
hal-01527749 , version 3 (10-11-2018)

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Jean-Marc Bardet, Paul Doukhan. Non-parametric estimation of time varying AR(1)–processes with local stationarity and periodicity. 2017. ⟨hal-01527749v2⟩
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