Building upon the previously introduced MVGC and PCMCI+ algorithms, we applied these methods to identify key causal variables of Arctic sea ice dynamics. For both daily and monthly datasets, MVGC identified all variables except Sea Surface T emperature (SST) as causal features. This result underscores the broad influence of atmospheric and oceanic variables on Arctic sea ice. PCMCI+, known for its robustness in handling high-dimensional and autocorrelated time series data, provided a more refined identification of causal features. For the daily dataset, PCMCI+ highlighted longwave radiation, snowfall, sea surface salinity (SSS), surface pressure, and SIE itself as the primary causal factors. For the monthly dataset, the identified causal features were longwave radiation, SST, and SIE . These results suggest temporal and spatial differences in the causal relationships influencing SIE dynamics across daily and monthly timescales. Figure 4 shows the causal graphs generated by PCMCI+ for daily and monthly datasets, highlighting the direct causal influences of key variables on Arctic SIE. The identified features guided the selection of input variables for the GRU-LSTM model, ensuring that the model leveraged causally significant information for prediction.

Time series data are found in many areas of healthcare such as medical time series, electronic health records (EHR), measurements of vitals, and wearable devices. Causal discovery, which involves estimating causal relationships from observational data, holds the potential to play a significant role in extracting actionable insights about human health. In this study, we present a novel constraint-based causal discovery approach for autocorrelated and non-stationary time series data (CDANs). Our proposed method addresses several limitations of existing causal discovery methods for autocorrelated and non-stationary time series data, such as high dimensionality, the inability to identify lagged causal relationships, and overlooking changing modules. Our approach identifies lagged and instantaneous/contemporaneous causal relationships along with changing modules that vary over time. The method optimizes the conditioning sets in a constraint-based search by considering lagged parents instead of conditioning on the entire past that addresses high dimensionality. The changing modules are detected by considering both contemporaneous and lagged parents. The approach first detects the lagged adjacencies, then identifies the changing modules and contemporaneous adjacencies, and finally determines the causal direction. We extensively evaluated our proposed method on synthetic and real-world clinical datasets, and compared its performance with several baseline approaches. The experimental results demonstrate the effectiveness of the proposed method in detecting causal relationships and changing modules for autocorrelated and non-stationary time series data.

Conventional temporal causal discovery (CD) methods suffer from high dimensionality, fail to identify lagged causal relationships, and often ignore dynamics in relations. In this study, we present a novel constraint-based CD approach for autocorrelated and non-stationary time series data (eCDANs) capable of detecting lagged and contemporaneous causal relationships along with temporal changes. eCDANs addresses high dimensionality by optimizing the conditioning sets while conducting conditional independence (CI) tests and identifies the changes in causal relations by introducing a surrogate variable to represent time dependency. Experiments on synthetic and real-world data show that eCDANs can identify time influence and outperform the baselines.