Multichannel Monte Carlo Singular Spectrum Analysis with Colored Noise Assessment

Abstract

Permanent GNSS stations continuously monitor Earth's crust movements in horizontal and vertical directions. The recorded data include deterministic variations, including linear trends, periodic signals, and offsets, alongside stochastic variations represented by various noise models. Accurately detecting deterministic behaviors depends on a realistic estimation of the observation noise model. A new multivariate algorithm based on Monte Carlo singular spectrum analysis (MCSSA) is developed to analyze the multiple channels of time-series data simultaneously (e.g., different position components or data from multiple stations), considering noise correlations without being limited to a specific noise model. Testing on simulated GNSS data showed that, by increasing the number of channels, the algorithm could accurately identify dominant annual and semiannual components in the presence of colored noise. The results also indicated that unrealistic assumptions about the GNSS position time-series noise model can be misleading in the MCSSA hypothesis testing. Applying the algorithm to real Greenland GNSS data confirmed the significance of annual and semiannual harmonic patterns when white plus flicker noise (FLWN) combinations were considered as the stochastic behavior of data. In the univariate analysis of the vertical position time series contaminated with random walk noise, none of the annual and semiannual signals were interpreted to be significant. At the same time, the proposed multivariate algorithm successfully identified the annual signal but lacked sufficient channels (stations) to confirm the significance of the semiannual signal in the presence of random walk noise. The multivariate analysis has confirmed the significance of semiannual signal across 21 time series contaminated with FLWN, which univariate analysis missed due to a high level of colored noise.