Understanding and modelling the properties of the stochastic variations in geodetic time series is crucial to obtain realistic uncertainties for deterministic parameters, e.g., long-term velocities, and helpful in characterizing non-modelled processes. With the increasing span of geodetic time series, it is expected that additional observations would help better understand the low-frequency properties of these stochastic variations. In the meantime, recent studies evidenced that the choice of the functional model for the time series biases the assessment of these low-frequency stochastic properties. In particular, frequent offsets in position time series can hinder the evaluation of the noise level at low frequencies and prevent the detection of possible random-walk-type variability. This study investigates the ability of the Maximum Likelihood Estimation (MLE) method to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. We show that part of the influence of offsets reported by previous studies results from the MLE method estimation biases. These biases occur even when all offset epochs are correctly identified and accounted for in the trajectory model. They can cause a dramatic underestimation of deterministic parameter uncertainties. We show that one can avoid biases using the Restricted Maximum Likelihood Estimation (RMLE) method. Yet, even when using the RMLE method or equivalent, adding offsets to the trajectory model inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than other stochastic parameters.

理解和建模大地时间序列中随机变化的特性对于获得确定性参数（例如长期速度）的实际不确定性至关重要，并且有助于表征非建模过程。随着大地时间序列跨度的增加，预计额外的观测将有助于更好地理解这些随机变化的低频特性。与此同时，最近的研究表明，时间序列的函数模型的选择会影响对这些低频随机特性的评估。特别是，位置时间序列中的频繁偏移会阻碍对低频噪声水平的评估，并阻止检测可能的随机游走类型的可变性。本研究调查了最大似然估计 (MLE) 方法在存在频繁偏移的情况下正确检索大地时间序列低频随机特性的能力。我们表明，先前研究报告的偏移量的部分影响来自 MLE 方法估计偏差。即使在轨迹模型中正确识别并考虑了所有偏移时期，这些偏差也会发生。它们可能导致对确定性参数不确定性的严重低估。我们表明，使用受限最大似然估计 (RMLE) 方法可以避免偏差。然而，即使使用 RMLE 方法或等效方法，