A unified neural framework for long-term time series forecasting and granger-style causal analysis

Reliable long-term time series forecasting (LTSF) in complex multivariate systems requires both effective long-range sequence modeling and informative analysis of cross-variable dependencies. Existing methods usually optimize these goals separately, leading to a mismatch between predictive performance and causal interpretability. To address this issue, we propose Mamba with Kolmogorov-Arnold Network and Jacobian Regularization (MKJR), a unified framework for mutual reinforcement between LTSF and Granger-style causal analysis. MKJR combines a Kolmogorov-Arnold Network (KAN)-based encoder-decoder with an asymmetric bidirectional dual-stream Mamba backbone. The KAN modules perform variable-wise nonlinear embedding and forecasting readout, while exposing encoder-side source-lag structural priors and decoder-side target-aware readout preferences. Built on this representation layer, the dual-stream Mamba captures fine-grained local temporal signatures and broader cross-variable dependency patterns within the same predictor. During training, MKJR uses a matrix-free random-projection Jacobian regularizer to constrain local sensitivity and encourage smoother, more target-relevant lagged predictive dependencies. During evaluation, MKJR fuses encoder-side priors, decoder-side readout preference, and Jacobian sensitivity into lag-resolved Granger-style dependence scores for graph recovery. In this way, better predictive representations provide more reliable dependence evidence, while dependence-aware regularization suppresses diffuse sensitivities and improves forecasting robustness. The resulting design is well suited to complex nonlinear multivariate systems with long forecasting horizons and distribution shifts. Experiments on multiple datasets across forecasting and causal analysis settings show that MKJR achieves the best overall performance and remains highly competitive on individual benchmarks, demonstrating practical value in complex industrial settings.