Related papers: Linear Prediction of Long-Memory Processes: Asympt…

In this paper we study the asymptotic behaviour of empirical processes when parameters are estimated, assuming that the underlying sequence of random variables is long-range dependent. We show completely different phenomena compared to…

Several applications in time series forecasting require predicting multiple steps ahead. Despite the vast amount of literature in the topic, both classical and recent deep learning based approaches have mostly focused on minimising…

This work aims at estimating inverse autocovariance matrices of long memory processes admitting a linear representation. A modified Cholesky decomposition is used in conjunction with an increasing order autoregressive model to achieve this…

Devising efficient algorithms to solve continuously-varying strongly convex optimization programs is key in many applications, from control systems to signal processing and machine learning. In this context, solving means to find and track…

Large and moderate deviation probabilities play an important role in many applied areas, such as insurance and risk analysis. This paper studies the exact moderate and large deviation asymptotics in non-logarithmic form for linear processes…

Motivated by the prevalence of environments in which data is abundant while resources for storage and/or transmission might be scarce, we study linear regression when predictors, their squares, and responses are subject to single-bit…

This paper develops asymptotic theory for estimation of parameters in regression models for binomial response time series where serial dependence is present through a latent process. Use of generalized linear model (GLM) estimating…

We consider the residual empirical process in random design regression with long memory errors. We establish its limiting behaviour, showing that its rates of convergence are different from the rates of convergence for to the empirical…

We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…

Nested-error regression models are widely used for analyzing clustered data. For example, they are often applied to two-stage sample surveys, and in biology and econometrics. Prediction is usually the main goal of such analyses, and…

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…

This paper studies the residual empirical process of long- and short-memory time series regression models and establishes its uniform expansion under a general framework. The results are applied to the stochastic regression models and…

Autonomous machine learning systems that learn many tasks in sequence are prone to the catastrophic forgetting problem. Mathematical theory is needed in order to understand the extent of forgetting during continual learning. As a…

This work develops non-asymptotic theory for estimation of the long-run variance matrix and its inverse, the so-called precision matrix, for high-dimensional time series under general assumptions on the dependence structure including…

In this paper we study different approaches for time series modeling. The forecasting approaches using linear models, ARIMA alpgorithm, XGBoost machine learning algorithm are described. Results of different model combinations are shown. For…

A recent article on generalised linear mixed model asymptotics, Jiang et al. (2022), derived the rates of convergence for the asymptotic variances of maximum likelihood estimators. If $m$ denotes the number of groups and $n$ is the average…

Advection-dominated dynamical systems, characterized by partial differential equations, are found in applications ranging from weather forecasting to engineering design where accuracy and robustness are crucial. There has been significant…

In this paper, we are interested in linear prediction of a particular kind of stochastic process, namely a marked temporal point process. The observations are event times recorded on the real line, with marks attached to each event. We show…

Data-driven methods for modeling dynamic systems have received considerable attention as they provide a mechanism for control synthesis directly from the observed time-series data. In the absence of prior assumptions on how the time-series…

In this work, we will investigate a Bayesian approach to estimating the parameters of long memory models. Long memory, characterized by the phenomenon of hyperbolic autocorrelation decay in time series, has garnered significant attention.…