# Amortized Interventional Forecasting for Multivariate CIR Processes

arXiv: https://arxiv.org/abs/2608.03715 · HTML: https://mlsanity.com/paper/2608.03715/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 14 of its 48 references that are in the map.
- First posted on arXiv 4 Aug 2026.

## Builds on (most cited first, 14 of 14)

- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [FFJORD: Free-form Continuous Dynamics for Scalable Reversible Generative Models](https://mlsanity.com/paper/1810.01367/) (2018)
- [Detecting causal associations in large nonlinear time series datasets](https://mlsanity.com/paper/1702.07007/) (2017)
- [Causal Discovery from Heterogeneous/Nonstationary Data with Independent Changes](https://mlsanity.com/paper/1903.01672/) (2019)
- [Estimating Counterfactual Treatment Outcomes over Time Through Adversarially Balanced Representations](https://mlsanity.com/paper/2002.04083/) (2020)
- [Transformer Neural Processes: Uncertainty-Aware Meta Learning Via Sequence Modeling](https://mlsanity.com/paper/2207.04179/) (2022)
- [Causal Transformer for Estimating Counterfactual Outcomes](https://mlsanity.com/paper/2204.07258/) (2022)
- [ForecastPFN: Synthetically-Trained Zero-Shot Forecasting](https://mlsanity.com/paper/2311.01933/) (2023)
- [CausalPFN: Amortized Causal Effect Estimation via In-Context Learning](https://mlsanity.com/paper/2506.07918/) (2025)
- [Estimating Interventional Distributions with Uncertain Causal Graphs through Meta-Learning](https://mlsanity.com/paper/2507.05526/) (2025)
- [Probabilistic Forecasting via Autoregressive Flow Matching](https://mlsanity.com/paper/2503.10375/) (2025)
- [Causal Time Series Generation via Diffusion Models](https://mlsanity.com/paper/2509.20846/) (2025)
- [CausalPlayground: Addressing Data-Generation Requirements in Cutting-Edge Causality Research](https://mlsanity.com/paper/2405.13092/) (2024)
- [Towards Causal Market Simulators](https://mlsanity.com/paper/2511.04469/) (2025)

## Abstract (arXiv)

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 correlated co-movement, not 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.