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Theory of Probability and Mathematical Statistics

Robust estimation for continuous-time linear models with memory

Mamikon S. Ginovyan, Artur A. Sahakyan

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Abstract: In time series analysis, much of 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 L\'evy-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.

Keywords: Trend; robust inference; L\'evy-driven continuous-time model; memory; smoothed periodogram; parametric and nonparametric estimation.

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