Inspectable Neural Markov Models for Non-Stationary Time Series
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2026
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| _version_ | 1866917547464458240 |
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| author | Rovirosa, Jan Schmolze, Jesse |
| author_facet | Rovirosa, Jan Schmolze, Jesse |
| contents | Modeling non-stationary stochastic systems requires balancing the representational capacity of deep learning with the structural transparency of classical probabilistic models. Markov transition matrices provide such a framework, but traditional frequency-based estimation collapses at high resolutions due to data sparsity. We propose a hybrid approach that parameterizes the manifold of stochastic matrices through a neural network, enabling estimation of time-inhomogeneous Markov chains in sparse-data regimes, and use financial markets as a testbed to investigate the Markov state variable as a critical inductive bias. We show that conditioning on realized volatility produces a more internally consistent Markovian structure than return-based states, achieving a $5.6\%$ reduction in Chapman-Kolmogorov discrepancy and superior held-out likelihood in 9 of 10 assets. Unlike black-box sequence models, our approach generates explicit matrices amenable to direct geometric analysis, surfacing structural findings such as the universal homogenization of transition probabilities under high-volatility regimes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_30943 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Inspectable Neural Markov Models for Non-Stationary Time Series Rovirosa, Jan Schmolze, Jesse Mathematical Finance Machine Learning Modeling non-stationary stochastic systems requires balancing the representational capacity of deep learning with the structural transparency of classical probabilistic models. Markov transition matrices provide such a framework, but traditional frequency-based estimation collapses at high resolutions due to data sparsity. We propose a hybrid approach that parameterizes the manifold of stochastic matrices through a neural network, enabling estimation of time-inhomogeneous Markov chains in sparse-data regimes, and use financial markets as a testbed to investigate the Markov state variable as a critical inductive bias. We show that conditioning on realized volatility produces a more internally consistent Markovian structure than return-based states, achieving a $5.6\%$ reduction in Chapman-Kolmogorov discrepancy and superior held-out likelihood in 9 of 10 assets. Unlike black-box sequence models, our approach generates explicit matrices amenable to direct geometric analysis, surfacing structural findings such as the universal homogenization of transition probabilities under high-volatility regimes. |
| title | Inspectable Neural Markov Models for Non-Stationary Time Series |
| topic | Mathematical Finance Machine Learning |
| url | https://arxiv.org/abs/2605.30943 |