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Non-parametric estimation of time varying AR(1)-processes with local stationarity and periodicity. (English) Zbl 1403.62155

Summary: Extending the ideas of [R. Dahlhaus, “Locally stationary processes”, in: Handbook of statistics. Time Series Analysis: Methods and Applications. Vol. 30. Amsterdam: North Holland (2012), arXiv:1109.4174], 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.

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
60F05 Central limit and other weak theorems
60G10 Stationary stochastic processes
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References:

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