Related papers: The Cointegrated Matrix Autoregressive Model

While artificial neural networks excel in unsupervised learning of non-sparse structure, classical statistical regression techniques offer better interpretability, in particular when sparseness is enforced by $\ell_1$ regularization,…

This article proposes novel estimation methods for the Matrix Autoregressive (MAR) model, specifically adaptations of the Yule-Walker equations and Burg's method, addressing limitations in existing techniques. The MAR model, by maintaining…

There has been a lot of recent interest in designing neural network models to estimate a distribution from a set of examples. We introduce a simple modification for autoencoder neural networks that yields powerful generative models. Our…

We propose a factor network autoregressive (FNAR) model for time series with complex network structures. The coefficients of the model reflect many different types of connections between economic agents ("multilayer network"), which are…

Representation learning is typically applied to only one mode of a data matrix, either its rows or columns. Yet in many applications, there is an underlying geometry to both the rows and the columns. We propose utilizing this coupled…

Modern technologies are producing a wealth of data with complex structures. For instance, in two-dimensional digital imaging, flow cytometry, and electroencephalography, matrix type covariates frequently arise when measurements are obtained…

In this paper we define and characterize cointegrated continuous-time linear state-space models. A main result is that a cointegrated continuous-time linear state-space model can be represented as a sum of a L\'evy process and a stationary…

We introduce \underline{F}actor-\underline{A}ugmented \underline{Ma}trix \underline{R}egression (FAMAR) to address the growing applications of matrix-variate data and their associated challenges, particularly with high-dimensionality and…

We propose a new class of spatio-temporal models with unknown and banded autoregressive coefficient matrices. The setting represents a sparse structure for high-dimensional spatial panel dynamic models when panel members represent economic…

The multivariate adaptive regression spline (MARS) is one of the popular estimation methods for nonparametric multivariate regressions. However, as MARS is based on marginal splines, to incorporate interactions of covariates, products of…

Matrix regression plays an important role in modern data analysis due to its ability to handle complex relationships involving both matrix and vector variables. We propose a class of regularized regression models capable of predicting both…

This paper proposes a Matrix Error Correction Model to identify cointegration relations in matrix-valued time series. We hereby allow separate cointegrating relations along the rows and columns of the matrix-valued time series and use…

Order-Agnostic autoregressive models have demonstrated strong performance in deep generative modeling, yet their use in settings with incomplete data remains largely unexplored. In this work, we reinterpret them through the lens of missing…

Repeated measures analyses require proper choice of the correlation model to ensure accurate inference and optimal efficiency. The linear exponent autoregressive (LEAR) correlation model provides a flexible two-parameter correlation…

Efficient estimation of high-dimensional matrices-including covariance and precision matrices-is a cornerstone of modern multivariate statistics. Most existing studies have focused primarily on the theoretical properties of the estimators…

Autoencoders are popular among neural-network-based matrix completion models due to their ability to retrieve potential latent factors from the partially observed matrices. Nevertheless, when training data is scarce their performance is…

Autoregressive models are ubiquitous tools for the analysis of time series in many domains such as computational neuroscience and biomedical engineering. In these domains, data is, for example, collected from measurements of brain activity.…

Mixed spatial autoregressive (SAR) models with numerical covariates have been well studied. However, as non-numerical data, such as functional data and compositional data, receive substantial amounts of attention and are applied to…

Modern technologies are producing datasets with complex intrinsic structures, and they can be naturally represented as matrices instead of vectors. To preserve the latent data structures during processing, modern regression approaches…

Autoregressive models capture stochastic processes in which past realizations determine the generative distribution of new data; they arise naturally in a variety of industrial, biomedical, and financial settings. A key challenge when…