Scalable Time Series Causal Discovery with Approximate Causal Ordering

Causal discovery in time series data presents a significant computational challenge. Standard algorithms are often prohibitively expensive for datasets with many variables or samples. This study introduces and validates a heuristic approximation of the VarLiNGAM algorithm to address this scalability problem. The standard VarLiNGAM method relies on an iterative refinement procedure for causal ordering that is computationally expensive. Our heuristic modifies this procedure by omitting the iterative refinement. This change permits a one-time precomputation of all necessary statistical values. The algorithmic modification reduces the time complexity of VarLiNGAM from $O\left(m^{3}n\right)$ to $O(m^{2}n+m^3)$ while keeping the space complexity at $O\left(m^2\right)$, where m is the number of variables and n is the number of samples. While an approximation, our approach retains VarLiNGAM’s essential structure and empirical reliability. On large-scale financial data with up to 400 variables, our algorithm achieves up to a 13.36× speedup over the standard implementation and an approximate 4.5× speedup over a GPU-accelerated version. Evaluations across medical time series analysis, IT service monitoring, and finance demonstrate the heuristic’s robustness and practical scalability. This work offers a validated balance between computational efficiency and discovery quality, making large-scale causal analysis feasible on personal computers.