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 Levy-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.
