Inspectable Neural Markov Models for Non-Stationary Time Series

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Hauptverfasser: Rovirosa, Jan, Schmolze, Jesse
Format: Preprint
Veröffentlicht: 2026
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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