P-stationary structural equation modeling: Causal effect identification under temporally incomplete observations
Abstract
Causal modeling of discrete-time processes often involves the assumption that the modeled processes are stationary. A general class of linear causal models for discrete-time stationary processes are structural equation processes (SEP), which generalize the well known structural equation model for i.i.d. observations. In this paper, we extend the SEP model from stationary to P-stationary processes, which are non-stationary processes whose P-periodically sampled subprocesses are jointly stationary. We will use this model to approach the problem of causal effect identification under temporally incomplete observations from a graphical modeling perspective. To have a notion of generic identifiability, we restrict our analysis to P-stationary structural vector autoregressive (SVAR) processes, which are SVAR processes whose underlying coefficients can vary P-periodically over time. Our findings allow to detect, in any given temporally incomplete observational setting, if a certain set of instrumental processes qualifies to identify a causal effect between P-periodic subprocesses, and if this is the case, that effect admits an explicit expression as a rational function evaluated at the observational spectral density.
Related
- Inferring physical fields in coupled systems with unknown parameters from incomplete observations using physics-constrained attentive neural operators
- UniGIO: Unified Generative Global In-situ Weather Modeling from Spatiotemporal Incomplete Observations
- Structural Compatibility and Uniform Stability of Temporally Degenerate Parabolic Systems
- Bi-HYCO: Bi-Objective Cooperative Learning for PDE Parameter Identification under Fragmented Observations
- Deep Bayesian Filtering for Nonlinear Structural System Identification: A Tutorial on Structural and Physical Inductive Biases
BibTeX
@misc{reiter2026pstationary,
title = {{$P$-stationary structural equation modeling: Causal effect identification under temporally incomplete observations}},
author = {Nicolas-Domenic Reiter},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.02252},
eprint = {2611.02252},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.02252},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - P-stationary structural equation modeling: Causal effect identification under temporally incomplete observations
AU - Nicolas-Domenic Reiter
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.02252
UR - https://arxiv.org/abs/2611.02252
AB - Causal modeling of discrete-time processes often involves the assumption that the modeled processes are stationary. A general class of linear causal models for discrete-time stationary processes are structural equation processes (SEP), which generalize the well known structural equation model for i.i.d. observations. In this paper, we extend the SEP model from stationary to P-stationary processes, which are non-stationary processes whose P-periodically sampled subprocesses are jointly stationary. We will use this model to approach the problem of causal effect identification under temporally incomplete observations from a graphical modeling perspective. To have a notion of generic identifiability, we restrict our analysis to P-stationary structural vector autoregressive (SVAR) processes, which are SVAR processes whose underlying coefficients can vary P-periodically over time. Our findings allow to detect, in any given temporally incomplete observational setting, if a certain set of instrumental processes qualifies to identify a causal effect between P-periodic subprocesses, and if this is the case, that effect admits an explicit expression as a rational function evaluated at the observational spectral density.
ER -