arXiv research

Novel estimation methods improve MAR model accuracy for high-dimensional time series.

Proposes a Structural Matrix Autoregressive model for joint analysis of asset returns, realized volatility, and trading volume.

Enhanced EEG classification using augmented covariance matrix.

Paper proposes a new MAR model for global economic forecasting.

BiGG model efficiently generates sparse graphs with reduced complexity.

High-dimensional time series data exist in numerous areas such as finance, genomics, healthcare, and neuroscience. An unavoidable aspect of all such datasets is missing data, and dealing with this issue has been an important focus in statistics, control, and machine learning. In this work, we consider a high-dimensiona…

We show Vector Autoregressive Moving Average models with scalar Moving Average components could be estimated by generalized least square (GLS) for each fixed moving average polynomial. The conditional variance of the GLS model is the concentrated covariant matrix of the moving average process. Under GLS the likelihood …

A new multivariate stochastic volatility estimation procedure for financial time series is proposed. A Wishart autoregressive process is considered for the volatility precision covariance matrix, for the estimation of which a two step procedure is adopted. The first step is the conditional inference on the autoregressi…

Study on estimating sparse transition matrix of partially-observed VAR with noisy and sparse data.

Tensor networks improve unsupervised learning performance.

Transformers become faster by linearizing self-attention.

We study sparse principal component analysis for high dimensional vector autoregressive time series under a doubly asymptotic framework, which allows the dimension $d$ to scale with the series length $T$. We treat the transition matrix of time series as a nuisance parameter and directly apply sparse principal component…

FLANDERS detects and blocks extreme model poisoning in federated learning.

Sparse Tucker decomposition with graph regularization improves time series forecasting accuracy.

Paper unifies subspace identification and DMD for dynamical systems.

New method for identifying graph shift operators using vertex-time autoregressive models.

Paper proposes LATC for multivariate time series prediction and missing data imputation.

New method for inferring network topology from partial data.

Survey of graph learning methods for combinatorial optimization problems.

New GLS estimator handles high-dimensional data with autocorrelated errors.

We show how to solve a number of problems in numerical linear algebra, such as least squares regression, $\ell_p$-regression for any $p \geq 1$, low rank approximation, and kernel regression, in time $T(A) \poly(\log(nd))$, where for a given input matrix $A \in \mathbb{R}^{n \times d}$, $T(A)$ is the time needed to com…

Improved covariance matrix forecasting for S&P 500 using factor models and shrinkage.

We introduce a concept of $autoregressive$ (AR)state-space realization that could be applied to all transfer functions $\boldsymbol{T}(L)$ with $\boldsymbol{T}(0)$ invertible. We show that a theorem of Kalman implies each Vector Autoregressive model (with exogenous variables) has a minimal $AR$-state-space realization …

FOCUS method forecasts counterfactuals in panel data with time series dynamics.

A widely applied approach to causal inference from a non-experimental time series $X$, often referred to as "(linear) Granger causal analysis", is to regress present on past and interpret the regression matrix $\hat{B}$ causally. However, if there is an unmeasured time series $Z$ that influences $X$, then this approach…

We study the problem of learning the support of transition matrix between random processes in a Vector Autoregressive (VAR) model from samples when a subset of the processes are latent. It is well known that ignoring the effect of the latent processes may lead to very different estimates of the influences among observe…

The purpose of this paper is to propose a time-varying vector autoregressive model (TV-VAR) for forecasting multivariate time series. The model is casted into a state-space form that allows flexible description and analysis. The volatility covariance matrix of the time series is modelled via inverted Wishart and singul…

New method for estimating and testing impulse responses in high-dimensional VAR systems.

We propose in this work a new family of kernels for variable-length time series. Our work builds upon the vector autoregressive (VAR) model for multivariate stochastic processes: given a multivariate time series x, we consider the likelihood function p_θ(x) of different parameters θin the VAR model as features to descr…

The vector autoregressive (VAR) model is a powerful tool in modeling complex time series and has been exploited in many fields. However, fitting high dimensional VAR model poses some unique challenges: On one hand, the dimensionality, caused by modeling a large number of time series and higher order autoregressive proc…

Estimates spatio-temporal data with satellite NO2 concentrations using Yule-Walker equations.

We introduce a novel multivariate random process producing Bernoulli outputs per dimension, that can possibly formalize binary interactions in various graphical structures and can be used to model opinion dynamics, epidemics, financial and biological time series data, etc. We call this a Bernoulli Autoregressive Proces…

Autoregressive models are among the best performing neural density estimators. We describe an approach for increasing the flexibility of an autoregressive model, based on modelling the random numbers that the model uses internally when generating data. By constructing a stack of autoregressive models, each modelling th…

A new method for filling in missing traffic data improves accuracy over existing techniques.

This work proposes an efficient autoregressive model for text generation.

In this paper, we study non-asymptotic deviation bounds of the least squares estimator in Gaussian AR($n$) processes. By relying on martingale concentration inequalities and a tail-bound for $χ^2$ distributed variables, we provide a concentration bound for the sample covariance matrix of the process output. With this, …

Autoregressive sequence models achieve state-of-the-art performance in domains like machine translation. However, due to the autoregressive factorization nature, these models suffer from heavy latency during inference. Recently, non-autoregressive sequence models were proposed to reduce the inference time. However, the…

Bayesian method for multivariate autoregressive models with exogenous inputs.

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex optimization. In each time window, we assume the data follow a linear model parameterized …

Autoregressive state transitions, where predictions are conditioned on past predictions, are the predominant choice for both deterministic and stochastic sequential models. However, autoregressive feedback exposes the evolution of the hidden state trajectory to potential biases from well-known train-test discrepancies.…

Alternative sampling method for autoregressive models using Langevin dynamics.

Paper proposes AXE loss for non-autoregressive machine translation, improving performance.

Spatial econometric research typically relies on the assumption that the spatial dependence structure is known in advance and is represented by a deterministic spatial weights matrix. Contrary to classical approaches, we investigate the estimation of sparse spatial dependence structures for regular lattice data. In par…

Linear attention in Transformers can be interpreted as dynamic VAR models.

Paper proposes a self-supervised method to denoise autoregressive signals with heavy-tailed noise.

Parallelizes autoregressive generation using VSSM.

We develop methods to estimate lag and parameters for multiple stable autoregressive processes.

Efficiently combines autoregressive and set-based models for joint distributions.