The problem of estimating the parameters of the continuous spectrum of a time series which might contain periodic components is studied. When a series contains periodic components, the periodogram ordinates at frequencies near the frequencies of the periodic components have significant amplitude, and can be viewed as outliers in an exponential sample. Three estimation procedures are proposed, which apply robust techniques on the periodogram ordinates to reduce the effect of the peaks. Under some regularity conditions, the asymptotic distributions of the estimates are derived. The proposed procedures have one major advantage that they do not need a precise model for the periodic components, and therefore can be applied when the periodic components are too complicated to model or when the number of the periodic components is unknown. The procedures are applied to a simulated series and the data set of the Canadian lynx trappings. An order selection criterion is also proposed.
