Scalable estimation of VARMA models2608.06340AuthorsDaniel Paulin,Victor ElviraAbstractVector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the parametrization is identified only up to equivalence, and every evaluation costs a pass over the entire series. Yet their moving-average term captures with a few parameters what a pure autoregression matches only with many lags. We introduce an estimation framework that removes this computational barrier: each optimization iteration is independent of the series length $T$. The framework combines a partial-autocorrelation reparametrization that guarantees stationarity and invertibility by construction, Gaussian priors on the reparametrized coefficients with separate scales for diagonal and off-diagonal entries, and losses that depend on the data only through fixed-size sufficient statistics, evaluated by a Parseval (Fourier) identity at near-linear cost in the truncation length. This yields two point estimators: a regularized least-squares fit and a covariance-marginalized maximum-a-posteriori estimator. We prove that both recover the infinite-autoregressive representation of the true process at a near-parametric rate in fixed dimension, so the truncation introduces no asymptotic bias. The same machinery extends, at the same leading cost, to seasonal dynamics, exogenous regressors (VARMAX), and rolling-window refits. Empirically, the estimators stay close to the oracle forecast error from $d=10$ to $d=40$ (where classical conditional MLE returns non-invertible fits whose forecasts diverge) and match or beat VAR, Bayesian-VAR, component-wise ARMA, and sparse-VARMA baselines on retail-demand, meteorological, and air-quality data. This brings likelihood-based VARMA estimation, at a per-iteration cost independent of the series length, to the problem sizes where practitioners have so far relied on VAR models.ResourcesView on Hugging FaceRead PDFArXiv
Scalable estimation of VARMA models
Vector autoregressive moving-average (VARMA) models have long been considered impractical beyond moderate dimensions: the likelihood is non-convex, the param...
Related
ResearchLearning When to Trust via Selective Context Preference Optimization
Language models increasingly condition their answers on external signals, and a single misleading one can turn a correct answer wrong. The obvious remedy, training models to resist such signals, hides a failure mode: a model that ignores all context looks robust yet is useless when the context is worth trusting. We recast the problem as selective trust and introduce MIST, a human-annotated benchmark that renders each reasoning item under four matched conditions (clean, misleading, correct-context, and irrelevant-context), together with SC2W, a paired metric counting how often a misle
Learning When to Trust via Selective Context Preference Optimization
Language models increasingly condition their answers on external signals, and a single misleading one can turn a correct answer wrong. The obvious remedy, tr...
ResearchTracing the Heart: An Evidence-Linked Pipeline for Heart-Failure Feature Engineering
Electronic health record (EHR) feature engineering is a major bottleneck in clinical research and AI, accounting for 39-45% of data scientists' workload. This is especially pronounced in heart failure, which affects an estimated 6.7 million U.S. adults and requires integrating fragmented EHR data with disease-specific, guideline-based clinical reasoning. Existing rule-based and large language model (LLM)-based approaches offer only partial automation with limited maintainability and evidence traceability. We developed the Nimblemind Multi-Agent System (nMAS), an evidence-linked, rubr