Electronic Journal of Statistics
- Electron. J. Statist.
- Volume 13, Number 1 (2019), 255-283.
Estimation of spectral functionals for Levy-driven continuous-time linear models with tapered data
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.
Electron. J. Statist., Volume 13, Number 1 (2019), 255-283.
Received: December 2017
First available in Project Euclid: 30 January 2019
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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