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MIDAS robust trend estimator for accurate GPS station velocities without step detection
Author(s) -
Blewitt Geoffrey,
Kreemer Corné,
Hammond William C.,
Gazeaux Julien
Publication year - 2016
Publication title -
journal of geophysical research: solid earth
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.983
H-Index - 232
eISSN - 2169-9356
pISSN - 2169-9313
DOI - 10.1002/2015jb012552
Subject(s) - estimator , outlier , statistics , global positioning system , mathematics , percentile , skewness , geodesy , classification of discontinuities , series (stratigraphy) , jackknife resampling , least squares function approximation , algorithm , computer science , geology , mathematical analysis , telecommunications , paleontology
Automatic estimation of velocities from GPS coordinate time series is becoming required to cope with the exponentially increasing flood of available data, but problems detectable to the human eye are often overlooked. This motivates us to find an automatic and accurate estimator of trend that is resistant to common problems such as step discontinuities, outliers, seasonality, skewness, and heteroscedasticity. Developed here, Median Interannual Difference Adjusted for Skewness (MIDAS) is a variant of the Theil‐Sen median trend estimator, for which the ordinary version is the median of slopes v ij = ( x j –x i )/( t j –t i ) computed between all data pairs i > j . For normally distributed data, Theil‐Sen and least squares trend estimates are statistically identical, but unlike least squares, Theil‐Sen is resistant to undetected data problems. To mitigate both seasonality and step discontinuities, MIDAS selects data pairs separated by 1 year. This condition is relaxed for time series with gaps so that all data are used. Slopes from data pairs spanning a step function produce one‐sided outliers that can bias the median. To reduce bias, MIDAS removes outliers and recomputes the median. MIDAS also computes a robust and realistic estimate of trend uncertainty. Statistical tests using GPS data in the rigid North American plate interior show ±0.23 mm/yr root‐mean‐square (RMS) accuracy in horizontal velocity. In blind tests using synthetic data, MIDAS velocities have an RMS accuracy of ±0.33 mm/yr horizontal, ±1.1 mm/yr up, with a 5th percentile range smaller than all 20 automatic estimators tested. Considering its general nature, MIDAS has the potential for broader application in the geosciences.