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.

Accurately predicting Earth’s rotation rate, as represented by Length of Day (LOD) variations, is essential for applications such as satellite navigation, climate studies, geophysical research, and disaster prevention. However, predicting LOD is challenging due to its sensitivity to various geophysical and meteorological factors. Current methods, including statistical approaches, often struggle with short-term forecasting accuracy. In this study, we use Monte Carlo Singular Spectrum Analysis (MCSSA) to distinguish between deterministic and non-deterministic components within the LOD time series. The deterministic components are extended using the SSA prediction algorithm. To enhance robustness, we refine Allen and Smith’s methodology (testing significance of eigenmodes against an autoregressive (AR) (1) noise null hypothesis) by integrating an autoregressive moving average (ARMA) model to account for noise, providing valuable insights into the non-deterministic behaviors present in the series. We comprehensively evaluate our methodology through a comparative analysis. For long-term prediction (365 days), we compare our method against the combined LS and autoregressive (AR) method. For short-term prediction (next 10 days), we compare it against the results of the second Earth Orientation Parameters Prediction Comparison Campaign (second EOP PCC). Using the IERS 20 C04 time series, our hybrid model demonstrates a superior long-term prediction accuracy with a mean absolute error (MAE) of 0.201 ms/day on the 365th day. Additionally, the short-term prediction performance is comparable to the second EOP PCC results. These results illustrate that the proposed method efficiently predicts LOD, showing significant improvement in long-term accuracy and robustness in short-term forecasting.