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Theory of Probability and Mathematical Statistics

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Robust estimation for continuous-time linear models with memory


Authors: Mamikon S. Ginovyan and Artur A. Sahakyan
Original publication: Teoriya Imovirnostei ta Matematichna Statistika, tom 95 (2016).
Journal: Theor. Probability and Math. Statist. 95 (2017), 81-98
MSC (2010): Primary 60F05, 60G22; Secondary 62G05, 62G20
DOI: https://doi.org/10.1090/tpms/1023
Published electronically: February 28, 2018
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Abstract: In time series analysis, much of the statistical inferences about unknown spectral parameters or spectral functionals are concerned with the discrete-time stationary models, in which case it is assumed that the models are centered, or have constant means. The present paper deals with a question involving robustness of inferences, carried out on Lévy-driven continuous-time linear models, possibly exhibiting long memory, contaminated by a small trend. We show that a smoothed periodogram approach to both parametric and nonparametric estimation is robust to the presence of a small trend in the model.


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Additional Information

Mamikon S. Ginovyan
Affiliation: Department of Mathematics and Statistics, Boston University, 111 Cummington Mall, Boston, Massachusetts 02215
Email: ginovyan@math.bu.edu

Artur A. Sahakyan
Affiliation: Department of Mathematics and Mechanics, Yerevan State University, 1 Alex Manoogian, Yerevan, 0025, Armenia
Email: sart@ysu.am

DOI: https://doi.org/10.1090/tpms/1023
Keywords: Trend, robust inference, L\'evy-driven continuous-time model, memory, smoothed periodogram, parametric and nonparametric estimation
Received by editor(s): October 17, 2016
Published electronically: February 28, 2018
Additional Notes: The research of the first author was partially supported by National Science Foundation Grant #DMS-1309009 at Boston University.
Article copyright: © Copyright 2018 American Mathematical Society

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