{"ID":2900875,"CreatedAt":"2026-06-01T05:51:17.9442275Z","UpdatedAt":"2026-06-01T06:23:29.641557848Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2605.30943","arxiv_id":"2605.30943","title":"Inspectable Neural Markov Models for Non-Stationary Time Series","abstract":"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.","short_abstract":"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 spars...","url_abs":"https://arxiv.org/abs/2605.30943","url_pdf":"https://arxiv.org/pdf/2605.30943v1","authors":"[\"Jan Rovirosa\",\"Jesse Schmolze\"]","published":"2026-05-29T07:29:35Z","proceeding":"q-fin.MF","tasks":"[\"q-fin.MF\",\"stat.ML\"]","methods":"[]","has_code":false}