A Unified Taxonomy of Modeling Paradigms: Linear, Nonlinear, Context-Variable, and Self-Directed Causal Frameworks with Theoretical Foundations and Empirical Validation

Abstract

This manuscript develops a unified taxonomy for modeling paradigms in complex, non-stationary systems, organizing linear, nonlinear, context-variable (regime-switching), and self-directed causal frameworks under a single structural causal model (SCM) formalism. Building on Markov-switching structural vector autoregression (MS-SVAR) theory, we present explicit assumptions, identifiability theorems, and a novel hybrid construct, the Causal Markov-Switching SCM (CMS-SCM), together with expanded, self-contained proofs. Every quantitative claim in this manuscript is the direct output of code executed during preparation of the manuscript: a Hamilton filter/Kim smoother expectation-maximization (EM) estimator for two- and three-regime MS-AR(1) models is implemented from first principles in NumPy/SciPy (no proprietary or unverifiable software), and is used to (i) recover regime parameters from synthetic data with 95% block-bootstrap confidence intervals, (ii) quantify one-step-ahead forecasting accuracy against both a linear AR(1) baseline and a genuine multilayer-perceptron neural-network baseline, (iii) recover regime-dependent causal structure in a four-variable synthetic system with a mean edge-recovery F1 of 0.993 ± 0.021 under oracle regime labels versus 0.708 ± 0.042 for a regime-blind pooled linear fit, (iv) characterize the empirical size and power of a moment-based linearity test, and (v) conduct a five-parameter global (Saltelli/Sobol) sensitivity analysis together with heavy-tailed-innovation and regime-order misspecification robustness checks, including a case in which information criteria favor an under-specified two-regime model over the true three-regime generating process. The regime-switching estimator reduces held-out mean-squared forecasting error by 12.1% relative to the linear baseline and 9.3% relative to the neural-network baseline. We further provide explicit Scientific and Technical Risk Assessment and Roadmap/Falsifiability sections that specify, for each central claim, the observation that would confirm or refute it.