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August 2019 Root-$n$ consistent estimation of the marginal density in semiparametric autoregressive time series models
Lionel Truquet
Bernoulli 25(3): 2107-2136 (August 2019). DOI: 10.3150/18-BEJ1047

Abstract

In this paper, we consider the problem of estimating the marginal density in some autoregressive time series models for which the conditional mean and variance have a parametric specification. Under some regularity conditions, we show that a kernel type estimate based on the residuals can be root-$n$ consistent even if the noise density is unknown. Our results substantially extend those existing in the literature. Our assumptions are carefully checked for some standard time series models such as ARMA or GARCH processes. Asymptotic expansion of our estimator is obtained by combining some martingale type arguments and a coupling method for time series which is of independent interest. We also study the uniform convergence of our estimator on compact intervals.

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Lionel Truquet. "Root-$n$ consistent estimation of the marginal density in semiparametric autoregressive time series models." Bernoulli 25 (3) 2107 - 2136, August 2019. https://doi.org/10.3150/18-BEJ1047

Information

Received: 1 August 2017; Revised: 1 April 2018; Published: August 2019
First available in Project Euclid: 12 June 2019

zbMATH: 07066251
MathSciNet: MR3961242
Digital Object Identifier: 10.3150/18-BEJ1047

Rights: Copyright © 2019 Bernoulli Society for Mathematical Statistics and Probability

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Vol.25 • No. 3 • August 2019
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