Related papers: Moving Aggregate Modified Autoregressive Copula-Ba…

As environments evolve, temporal distribution shifts can degrade time series forecasting performance. A straightforward solution is to adapt to nonstationary changes while preserving stationary dependencies. Hence, some methods disentangle…

The analysis of tabular data has traditionally been dominated by gradient-boosted decision trees (GBDTs), known for their proficiency with mixed categorical and numerical features. However, recent deep learning innovations are challenging…

Using a proper model to characterize a time series is crucial in making accurate predictions. In this work we use time-varying autoregressive process (TVAR) to describe non-stationary time series and model it as a mixture of multiple stable…

A novel probabilistic framework for modelling anomalous diffusion is presented. The resulting process is Markovian, non-homogeneous, non-stationary, non-ergodic, and state-dependent. The fundamental law governing this process is driven by…

Understanding the time-varying structure of complex temporal systems is one of the main challenges of modern time series analysis. In this paper, we show that every uniformly-positive-definite-in-covariance and sufficiently short-range…

Thanks to their ability to capture complex dependence structures, copulas are frequently used to glue random variables into a joint model with arbitrary marginal distributions. More recently, they have been applied to solve statistical…

This paper introduces a novel approach, the bivariate generalized autoregressive (BGAR) model, for modeling and forecasting bivariate time series data. The BGAR model generalizes the bivariate vector autoregressive (VAR) models by allowing…

I present an approach for modeling areal spatial covariance by considering the stationary distribution of a spatio-temporal Markov random walk. In the areal data case, this stationary distribution corresponds to an intrinsic simultaneous…

In environmental epidemiology studies, health response data (e.g. hospitalization or mortality) are often noisy because of hospital organization and other social factors. The noise in the data can hide the true signal related to the…

Diffusion models have achieved remarkable success as generative models. However, even a well-trained model can accumulate errors throughout the generation process. These errors become particularly problematic when arbitrary guidance is…

This is a survey of some recent results on the rational circulant covariance extension problem: Given a partial sequence $(c_0,c_1,\dots,c_n)$ of covariance lags $c_k=\mathbb{E}\{y(t+k)\overline{y(t)}\}$ emanating from a stationary periodic…

Generalized autoregressive moving average (GARMA) models are a class of models that was developed for extending the univariate Gaussian ARMA time series model to a flexible observation-driven model for non-Gaussian time series data. This…

Recent financial disasters have emphasised the need to accurately predict extreme financial losses and their consequences for the institutions belonging to a given financial market. The ability of econometric models to predict extreme…

We prove that a time series satisfying a (linear) multivariate autoregressive moving average (VARMA) model satisfies the same model assumption in the reversed time direction, too, if all innovations are normally distributed. This…

Copula models are widely employed in multivariate time series analysis because they permit flexible modelling of marginal distributions independently of the dependence structure, which is fully characterised by the copula function. However,…

Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less…

Temporal coherence-persistent alignment across time-can arise between agents with fundamentally distinct dynamics, a behavior that classical diffusion models (e.g., Brownian motion, fractional Brownian motion, generalized Langevin equation)…

Hierarchical models for regionally aggregated disease incidence data commonly involve region specific latent random effects that are modeled jointly as having a multivariate Gaussian distribution. The covariance or precision matrix…

We study stochastic ordering of system lifetimes with dependent and heterogeneous components whose marginal distributions are obtained through transformations of a common baseline. The dependence structure is modeled via Archimedean…

We propose a flexible model for count time series which has potential uses for both underdispersed and overdispersed data. The model is based on the Conway-Maxwell-Poisson (COM-Poisson) distribution with parameters varying along time to…