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Pré-Publication, Document De Travail Année : 2024

Nonparametric Estimation in Nonlinear Time-varying Autoregressive Locally Stationary Processes with ARCH-errors

Estimation non paramétrique pour un processus auto-régressif non linéaire variant avec le temps avec erreurs de type ARCH et qui est localement stationnaire

Résumé

This paper investigates the asymptotic properties of the Kernel estimators for the conditional mean and variance functions in a time-varying nonlinear autoregressive locally stationary process with ARCH errors (tvNAR) of order d > 1. We establish the uniform almost sure consistency for these estimators with rate under assumptions of local stationarity and local ergodicity. Special attention is also paid to the Kernel density estimation of the tvNAR process. The results are derived without assuming a specific type of mixing conditions or a particular physical dependence measure on the data. Consequently, our results are applicable to a wide range of dependent processes, including those satisfying strong mixing conditions.
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Dates et versions

hal-04611601 , version 1 (13-06-2024)
hal-04611601 , version 2 (21-08-2024)

Identifiants

  • HAL Id : hal-04611601 , version 1

Citer

Abderrahim Bourhattas, Naâmane Laïb. Nonparametric Estimation in Nonlinear Time-varying Autoregressive Locally Stationary Processes with ARCH-errors. 2024. ⟨hal-04611601v1⟩
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