Maximum Likelihood Estimation of the Vector AutoRegressive To Anything (VARTA) model

2025-11-29

AI Summary

Existing multivariate time series modeling approaches are often restricted to Gaussian assumptions or specific application domains, failing to simultaneously achieve general-purpose temporal dynamics modeling and arbitrary marginal distribution modeling. This paper proposes VARTA (Variational Autoregressive Transformation Architecture), a unified probabilistic framework that employs a latent Gaussian vector autoregressive (VAR) backbone and couples temporal dependence structure with non-Gaussian marginal distributions via invertible probabilistic transformations. Built upon maximum likelihood estimation and latent variable inference, VARTA enables predictive distribution computation, model diagnostics, and statistical hypothesis testing. Experiments demonstrate that VARTA significantly improves both accuracy and robustness of predictive distribution estimation under non-Gaussian settings. By unifying expressive temporal dependency modeling with flexible marginal distribution representation, VARTA establishes a theoretically rigorous yet broadly applicable paradigm for multivariate time series analysis.

Technology Category

• Reasoning under Uncertainty: Relational Probabilistic Models
• Machine Learning: Probabilistic Circuits and Graphical Models
• Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Graph embeddings and representation learning for Web-related graphs
• Web Mining and Content Analysis: Models for Web evolution
• User Modeling, Personalization and Recommendation: Explainable and interpretable methods for personalization

Abstract

The literature on multivariate time series is, largely, limited to either models based on the multivariate Gaussian distribution or models specifically developed for a given application. In this paper we develop a general approach which is based on an underlying, unobserved, Gaussian Vector Autoregressive (VAR) model. Using a transformation, we can capture the time dynamics as well as the distributional properties of a multivariate time series. The model is called the Vector AutoRegressive To Anyting (VARTA) model and was originally presented by Biller and Nelson (2003) who used it for the purpose of simulation. In this paper we derive a maximum likelihood estimator for the model and investigate its performance. We also provide diagnostic analysis and how to compute the predictive distribution. The proposed approach can provide better estimates about the forecasting distributions which can be of every kind not necessarily Gaussian distributions as for the standard VAR models.

Problem

• Estimates multivariate time series with non-Gaussian distributions
• Derives maximum likelihood estimator for VARTA model
• Provides forecasting distributions beyond standard VAR models

Innovation

• Maximum likelihood estimation for VARTA model
• Underlying Gaussian VAR with transformation approach
• Captures time dynamics and distributional properties