Electronic Journal of Statistics

Estimation of spectral functionals for Levy-driven continuous-time linear models with tapered data

Mamikon S. Ginovyan and Artur A. Sahakyan

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Abstract

The paper is concerned with the nonparametric statistical estimation of linear spectral functionals for Lévy-driven continuous-time stationary linear models with tapered data. As an estimator for unknown functional we consider the averaged tapered periodogram. We analyze the bias of the estimator and obtain sufficient conditions assuring the proper rate of convergence of the bias to zero, necessary for asymptotic normality of the estimator. We prove a a central limit theorem for a suitable normalized stochastic process generated by a tapered Toeplitz type quadratic functional of the model. As a consequence of these results we obtain the asymptotic normality of our estimator.

Article information

Source
Electron. J. Statist., Volume 13, Number 1 (2019), 255-283.

Dates
Received: December 2017
First available in Project Euclid: 30 January 2019

Permanent link to this document
https://projecteuclid.org/euclid.ejs/1548817591

Digital Object Identifier
doi:10.1214/18-EJS1525

Mathematical Reviews number (MathSciNet)
MR3905127

Zentralblatt MATH identifier
07021705

Subjects
Primary: 62F12: Asymptotic properties of estimators 62G20: Asymptotic properties
Secondary: 60G10: Stationary processes 60F05: Central limit and other weak theorems

Keywords
Lévy-driven continuous-time model tapered data smoothed periodogram central limit theorem nonparametric estimation asymptotic normality Toeplitz type quadratic functional

Rights
Creative Commons Attribution 4.0 International License.

Citation

Ginovyan, Mamikon S.; Sahakyan, Artur A. Estimation of spectral functionals for Levy-driven continuous-time linear models with tapered data. Electron. J. Statist. 13 (2019), no. 1, 255--283. doi:10.1214/18-EJS1525. https://projecteuclid.org/euclid.ejs/1548817591


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