The M-regression estimator has recently been widely used to build spectral estimators in time series models. In this paper, we extend this approach when the data follow a periodic autoregressive moving average process. We introduce an estimator of the parameters based on the classical Whittle estimator. The finite sample size performances of the proposed estimator are analyzed under the scenarios of PARMA processes with and without additive outliers. Under the non-contaminated scenario, our estimator and the maximum Gaussian and Whittle likelihood estimators have similar behaviors. However, in the contaminated case, the two last estimators are severely biased, while the proposed estimator is robust. As a real data application, carbon monoxide concentrations are analyzed. A PARMA model is fitted and the data are forecasted with the model.

在中号回归估计器最近已广泛用于在时间序列模型中构建频谱估计器。在本文中，当数据遵循周期性自回归移动平均过程时，我们扩展了这种方法。我们介绍基于经典Whittle估计器的参数估计器。在有或没有加法异常值的情况下，在PARMA过程的情况下，分析了所提出估计量的有限样本量性能。在无污染的情况下，我们的估计量以及最大高斯和惠特尔似然估计量具有相似的行为。但是，在受污染的情况下，最后两个估计量存在严重偏差，而建议的估计量却很健壮。作为真实的数据应用，分析一氧化碳浓度。拟合PARMA模型，并使用该模型预测数据。