Mean square consistency and improved rate of convergence of generalized subsampling estimator for nonstationary time series - Archive ouverte HAL
Pré-Publication, Document De Travail Année : 2024

Mean square consistency and improved rate of convergence of generalized subsampling estimator for nonstationary time series

Résumé

In this paper, we show the mean square consistency for a generalized subsampling estimator based on the aggregation of the mean, median, and trimmed mean of some subsampling estimators for general nonstationary time series. Consistency requires standard assumptions, including the existence of moments and α-mixing conditions. We apply our results to the Fourier coefficients of the autocovariance function of periodically correlated time series. Furthermore, as in the i.i.d. case, we show that the generalized subsampling estimator satisfies Bernstein inequality and concentrates at an improved rate (under the condition of no or small bias) compared to the original estimator. Finally, we illustrate our results with some simulation data examples.
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Dates et versions

hal-04736236 , version 1 (14-10-2024)

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  • HAL Id : hal-04736236 , version 1

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Patrice Bertail, Anna E. Dudek, Lukasz Lenart. Mean square consistency and improved rate of convergence of generalized subsampling estimator for nonstationary time series. 2024. ⟨hal-04736236⟩
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