Related papers: Spectral analysis of long range dependence functio…

Long-range correlated processes are ubiquitous, ranging from climate variables to financial time series. One paradigmatic example for such processes is fractional Brownian motion (fBm). In this work, we highlight the potentials and…

Function-on-function regression has been a topic of substantial interest due to its broad applicability, where the relation between functional predictor and response is concerned. In this article, we propose a new framework for modeling the…

Time series foundation models have shown impressive performance on a variety of tasks, across a wide range of domains, even in zero-shot settings. However, most of these models are designed to handle short univariate time series as an…

We consider multivariate copula-based stationary time-series under Gaussian subordination. Observed time series are subordinated to long-range dependent Gaussian processes and characterized by arbitrary marginal copula distributions. First…

In this article, we aim to further clarify certain subtle aspects of processes that exhibit long memory in the second-order sense. We construct a long-memory stochastic sequence, in the sense that the series of absolute autocovariances…

In this paper, we propose methods for functional predictor selection and the estimation of smooth functional coefficients simultaneously in a scalar-on-function regression problem under high-dimensional multivariate functional data setting.…

Functional time series have become an integral part of both functional data and time series analysis. Important contributions to methodology, theory and application for the prediction of future trajectories and the estimation of functional…

We study estimation of a multivariate function $f:\mathbf{R}^d\to\mathbf{R}$ when the observations are available from the function $Af$, where $A$ is a known linear operator. Both the Gaussian white noise model and density estimation are…

In linear models, omitting a covariate that is orthogonal to covariates in the model does not result in biased coefficient estimation. This in general does not hold for longitudinal data, where additional assumptions are needed to get…

We develop a generalization of correlated trend-cycle decompositions that avoids prior assumptions about the long-run dynamic characteristics by modelling the permanent component as a fractionally integrated process and incorporating a…

We consider the almost sure asymptotic behavior of the periodogram of stationary and ergodic sequences. Under mild conditions we establish that the limsup of the periodogram properly normalized identifies almost surely the spectral density…

Establishing causality is a fundamental goal in fields like medicine and social sciences. While randomized controlled trials are the gold standard for causal inference, they are not always feasible or ethical. Observational studies can…

We consider the problem of estimating the slope parameter in functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of second order stationary random functions X1,...,Xn. An orthogonal series estimator of…

Spectral networks derived from multivariate time series data arise in many domains, from brain science to Earth science. Often, it is of interest to study how these networks change under different conditions. For instance, to better…

We develop a geometric account of sequence modelling that links patterns in the data to measurable properties of the loss landscape in transformer networks. First, we cast conditional sequence distributions into a Hilbert-space framework…

We focus on the problem estimating a monotone trend function under additive and dependent noise. New point-wise confidence interval estimators under both short- and long-range dependent errors are introduced and studied. These intervals are…

We study long-time behaviors for branching-diffusion process corresponding to the drifted Schr\"odinger operator $\mathcal{L} = \frac{1}{2} \Delta + \langle \nabla V,\nabla \rangle - K$, where $K$ represents the reduction rate of a…

We consider the problem of learning a classifier from observed functional data. Here, each data-point takes the form of a single time-series and contains numerous features. Assuming that each such series comes with a binary label, the…

This paper addresses estimation in a longitudinal regression model for association between a scalar outcome and a set of longitudinally-collected functional covariates or predictor curves. The framework consists of estimating a time-varying…

The problem of domain generalization is to learn, given data from different source distributions, a model that can be expected to generalize well on new target distributions which are only seen through unlabeled samples. In this paper, we…