Impact of offsets on assessing the low-frequency stochastic properties of geodetic time series

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.