Related papers: ARMA Time-Series Modeling with Graphical Models

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…

The autoregressive (AR) model is a widely used model to understand time series data. Traditionally, the innovation noise of the AR is modeled as Gaussian. However, many time series applications, for example, financial time series data, are…

Time series often exhibit non-ergodic behaviour that complicates forecasting and inference. This article proposes a likelihood-based approach for estimating ergodicity transformations that addresses such challenges. The method is broadly…

This paper considers quantile regression for a wide class of time series models including ARMA models with asymmetric GARCH (AGARCH) errors. The classical mean-variance models are reinterpreted as conditional location-scale models so that…

Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…

Dynamic linear models (DLM) offer a very generic framework to analyse time series data. Many classical time series models can be formulated as DLMs, including ARMA models and standard multiple linear regression models. The models can be…

Modeling complex dynamical systems under varying conditions is computationally intensive, often rendering high-fidelity simulations intractable. Although reduced-order models (ROMs) offer a promising solution, current methods often struggle…

This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…

In many applications, the variables that characterize a stochastic system are measured along a second dimension, such as time. This results in multivariate functional data and the interest is in describing the statistical dependences among…

Forecasting time series data is an important subject in economics, business, and finance. Traditionally, there are several techniques to effectively forecast the next lag of time series data such as univariate Autoregressive (AR),…

We study the quadratic prediction error method -- i.e., nonlinear least squares -- for a class of time-varying parametric predictor models satisfying a certain identifiability condition. While this method is known to asymptotically achieve…

Multivariate time series analysis is becoming an integral part of data analysis pipelines. Understanding the individual time point connections between covariates as well as how these connections change in time is non-trivial. To this aim,…

Generative moment matching networks (GMMNs) are suggested for modeling the cross-sectional dependence between stochastic processes. The stochastic processes considered are geometric Brownian motions and ARMA-GARCH models. Geometric Brownian…

Optimizing machine learning algorithms that are used to solve the objective function has been of great interest. Several approaches to optimize common algorithms, such as gradient descent and stochastic gradient descent, were explored. One…

Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…

The autologistic actor attribute model, or ALAAM, is the social influence counterpart of the better-known exponential-family random graph model (ERGM) for social selection. Extensive experience with ERGMs has shown that the problem of…

In the past four decades, research on count time series has made significant progress, but research on $\mathbb{Z}$-valued time series is relatively rare. Existing $\mathbb{Z}$-valued models are mainly of autoregressive structure, where the…

One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering…

Nonlinear relationships between covariates and a response variable of interest are frequently encountered in animal science research. Within statistical models, these nonlinear effects have, traditionally, been handled using a range of…

Linear processes on functional spaces were born about fifteen years ago. And this original topic went through the same fast development as the other areas of functional data modeling such as PCA or regression. They aim at generalizing to…