Amortized Interventional Forecasting for Multivariate CIR Processes

2026-08-04

AI Summary

This study addresses the limitation of traditional multivariate CIR models, which capture only correlations among variables and cannot support counterfactual forecasting or stress testing under external interventions. To overcome this, the authors propose an amortized causal effect estimation framework that, for the first time, endows the multivariate CIR data-generating process with explicit causal structure by treating trajectories as timestamped observations. This approach enables efficient multi-step calibrated impulse response prediction without retraining for each intervention scenario. Integrating causal inference, amortized inference, and multivariate CIR stochastic differential equations, the model is trained on intervention-observation pairs from synthetic data. Experiments demonstrate strong causal identification and calibration performance on synthetic benchmarks, and in backtesting on real-world CDS spreads, it significantly outperforms baseline methods—particularly in short-term prediction horizons.

Abstract

Mean-reverting dynamics are pervasive in finance, and the Cox--Ingersoll--Ross (CIR) process is a standard model for the time series they produce, from short rates to credit default swap (CDS) spreads. Yet CIR models capture only \emph{correlated} co-movement, not \emph{causal} influence between series, so they cannot answer the system's response when one series is externally shocked, which observational conditionals confound with historical co-movement. We make two contributions. First, an amortized model for distributional causal effect estimation that frames trajectories as time-stamped observations and predicts the calibrated multi-horizon shock response without retraining per scenario. Second, a causal multivariate CIR data-generating process that supplies the paired observational and interventional ground truth that real markets cannot. We instantiate and calibrate the framework on CDS spreads as a testbed. CIR-ACTIVA's validity is established on synthetic ground truth, independent of how well the simulator matches reality, while practical grounding is assessed by backtesting the generated traces against real CDS data. Against observational and amortized causal-inference baselines, CIR-ACTIVA leads on both causal selectivity in the joint distribution and horizon-resolved calibration, retaining its selectivity once the interventional law varies over the horizon, with gains concentrating at short horizons. This opens up a class of what-if queries on coupled spread systems, CDS stress testing among them, that observational forecasters cannot answer.

Problem

• CIR process
• causal inference
• interventional forecasting
• multivariate time series
• what-if queries

Innovation

• amortized causal inference
• multivariate CIR process
• interventional forecasting
• causal effect estimation
• CDS spreads