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# On the application of Monte Carlo singular spectrum analysis to GPS position time series

### Abstract

Singular spectrum analysis (SSA) has recently been applied to various geodetic time series studies. As a data-adaptive method, SSA is capable of extracting signals with non-constant phase and amplitudes. Although SSA is a competent method in the presence of white noise, the contribution of colored noise, having semi-periodic behavior, degrades its performance. Parts of colored noise can be absorbed in the SSA eigenmodes, which specifies signals and hence resulting in spurious modulation or losing significant signals. Signals and colored noise are thus to be discriminated in the signal identification procedure. Monte Carlo SSA (MCSSA) in its original formulation, providing a significance test against the AR(1) noise null hypothesis, can be misinterpreted when other colored noise structures contribute to the series. We propose an algorithm for MCSSA that is not limited to the AR(1) noise hypothesis. It estimates the noise model parameters using LS-VCE and generates the surrogate data using the Cholesky decomposition. The algorithm is adapted to GPS position time series where the underlying noise is a combination of white noise and flicker noise. GPS position time series, postulated real situation, are first simulated to include annual and semiannual signals plus white and flicker noise. The results indicate that MCSSA can extract the annual and semiannual signals with 2.11 and 1.25 mm amplitudes (the global mean values) from 20-year-long time series, with 95% confidence level, if flicker noise is less than 17 and 13

$${\text{mm/year}}^{1/4}$$

, respectively. The longer the time series or the stronger the signals are, the higher these thresholds will be. This conclusion is also verified when applying MCSSA to the up component of GPS position time series of 347 JPL stations.

from Latest Results for Journal of Geodesy http://link.springer.com/10.1007/s00190-019-01253-x

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