SEAM: Recovering Causal Reversals Across Recurring Regimes

Many systems switch between a few recurring states whose causal relations partly differ: some relations stay the same, while others reverse direction. From one multivariate time series with unknown state boundaries, we ask when the state changes, which causal relations change, and what an intervention would do in each state. We introduce SEAM (Shared Equations Across Mechanisms), which jointly learns the recurring states, a causal graph for each, and which structural equations the states share. Separate causal orders let an effect reverse; estimating the unchanged equations from both states improves precision. One description-length score decides between no change, a change in noise levels only, and a change in the causal mechanisms, and a resampling test reruns the entire search on surrogate series to assess the evidence for a change. We give conditions under which the decision is consistent, both for Gaussian VAR series without a change and for mechanism changes that no change in noise levels can mimic, and we show that a row-permutation variant of the test controls its level at every sample size for exchangeable observations without lags. On five-variable systems with a reversal, SEAM's error on the reversed effects is 0.016 at the larger effect size, compared with 0.406–1.000 for five regime-aware baselines, and over all 640 series it finds the changed equations with F1 0.951; on 1400 series without a change, it reports a mechanism change in 0.36% of them. On five public daily river series, SEAM recovers the seasons in all 3 four-year windows, and in 2 of them the fitted influence between the Columbia and the Willamette reverses with the season, as hydrological studies describe.