Abstract.In this paper we are concerned with the robustness of inferences, carried out on a stationary process contaminated by a small trend, to this departure from stationarity. It is shown that a smoothed periodogram approach to model fining and parameter estimation is highly robust to the presence of a small trend if the underlying stationary process is short‐range dependent. If the underlying process is long‐range dependent the robustness properties are still good but now depend on the Hurst index of the process and deteriorate with increasing Hurst in
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