Impact of Offsets on Assessing the Low-Frequency Stochastic Properties of Geodetic Time Series

<p>Understanding and modelling the properties of the stochastic variability -- often referred to as noise -- 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 ever-increasing span of geodetic time series, it is expected that additional observations would help better understanding the low-frequency properties of the stochastic variability. In the meantime, recent studies evidenced that the choice of the functional model for the time series may bias the assessment of these low-frequency stochastic properties. In particular, the presence of frequent offsets, or step discontinuities, in position time series tends to systematically flatten the periodogram of position residuals at low frequencies and prevents the detection of possible random-walk-type variability.</p><p>&#160;</p><p>In this study, we investigate the ability of frequently-used statistical tools, namely the Lomb-Scargle periodogram and Maximum Likelihood Estimation (MLE) method, to correctly retrieve low-frequency stochastic properties of geodetic time series in the presence of frequent offsets. By evaluating the biases of each method for several functional models, we demonstrate that neither of these tools is reliable for low-frequency investigation. By assessing alternative approaches, we show that using &#160;Least-Squares Harmonic Estimation and Restricted Maximum Likelihood Estimation (RMLE) solves part of the problems reported by previous works. However, we evidence that, even when using those optimal methods, the presence of frequent offsets inevitably blurs the estimated low-frequency properties of geodetic time series by increasing low-frequency stochastic parameter uncertainties more than that of other stochastic parameters.</p><div>2.14.0.0</div><div></div><div>2.14.0.0</div>