Related papers: Quantile Time Series Regression Models Revisited
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
In this paper, we develop a new and effective approach to nonparametric quantile regression that accommodates ultrahigh-dimensional data arising from spatio-temporal processes. This approach proves advantageous in staving off computational…
We study stationarity and moments properties of some count time series models from contraction and stability properties of iterated random maps. Both univariate and multivariate processes are considered, including the recent multivariate…
Different disciplines pursue the aim to develop models which characterize certain phenomena as accurately as possible. Climatology is a prime example, where the temporal evolution of the climate is modeled. In order to compare and improve…
Nonlinear systems with model uncertainty are often described by stochastic differential equations. Some techniques from random dynamical systems are discussed. They are relevant to better understanding of solution processes of stochastic…
In 1980 and 1981, two pioneering papers laid the foundation for what became known as nonlinear time-series analysis: the analysis of observed data---typically univariate---via dynamical systems theory. Based on the concept of state-space…
In this paper the problems of the retrospective analysis of models with time-varying structure are considered. These models include contamination models with randomly switching parameters and multivariate classification models with an…
In recent years there has been a substantial increase in the availability of datasets which contain information about the location and timing of an event or group of events and the application of methods to analyse spatio-temporal datasets…
High-dimensional time series datasets are becoming increasingly common in many areas of biological and social sciences. Some important applications include gene regulatory network reconstruction using time course gene expression data, brain…
We survey current developments in the approximation theory of sequence modelling in machine learning. Particular emphasis is placed on classifying existing results for various model architectures through the lens of classical approximation…
These notes are intended as an introduction to a study of applications of noncommutative calculus to quantum statistical Physics. Centered on noncommutative calculus we describe the physical concepts and mathematical structures appearing in…
This is an annotated bibliography on estimation and inference results for queues and related stochastic models. The purpose of this document is to collect and categorise works in the field, allowing for researchers and practitioners to…
Modelling spatio-temporal processes has become an important issue in current research. Since Gaussian processes are essentially determined by their second order structure, broad classes of covariance functions are of interest. Here, a new…
A generic non-integrable (unitary) out-of-equilibrium quantum process, when interrogated across many times, is shown to yield the same statistics as an (non-unitary) equilibrated process. In particular, using the tools of quantum stochastic…
This paper considers a nonlinear quantile model with change-points. The quantile estimation method, which as a particular case includes median model, is more robust with respect to other traditional methods when model errors contain…
Quantile regression models provide a wide picture of the conditional distributions of the response variable by capturing the effect of the covariates at different quantile levels. In most applications, the parametric form of those…
This brief article gives an overview of quantum mechanics as a {\em quantum probability theory}. It begins with a review of the basic operator-algebraic elements that connect probability theory with quantum probability theory. Then quantum…
Linear quantile regression models aim at providing a detailed and robust picture of the (conditional) response distribution as function of a set of observed covariates. Longitudinal data represent an interesting field of application of such…
The availability of large amounts of time series data, paired with the performance of deep-learning algorithms on a broad class of problems, has recently led to significant interest in the use of sequence-to-sequence models for time series…
In this paper we survey some recent results on the central limit theorem and its weak invariance principle for stationary sequences. We also describe several maximal inequalities that are the main tool for obtaining the invariance…