Related papers: Functional Time Series
We consider functional data which have only been observed on a subset of their domain. This paper aims to develop statistical tests to determine whether the function and the domain over which it is observed are independent. The assumption…
We investigate the use of iterated function system (IFS) models for data analysis. An IFS is a discrete dynamical system in which each time step corresponds to the application of one of a finite collection of maps. The maps, which represent…
We introduce a novel class of nonlinear tests for serial dependence in functional time series, grounded in the functional quantile autocorrelation framework. Unlike traditional approaches based on the classical autocovariance kernel, the…
We present a holistic, topology-based visualization technique for spatial time series data based on an adaptation of Fuzzy Contour Trees. Common analysis approaches for time dependent scalar fields identify and track specific features. To…
Functional data clustering is to identify heterogeneous morphological patterns in the continuous functions underlying the discrete measurements/observations. Application of functional data clustering has appeared in many publications across…
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…
Time series data, defined by equally spaced points over time, is essential in fields like medicine, telecommunications, and energy. Analyzing it involves tasks such as classification, clustering, prototyping, and regression. Classification…
Study of time series data often involves measuring the strength of temporal dependence, on which statistical properties like consistency and central limit theorem are built. Historically, various dependence measures have been proposed. In…
Roughly speaking, functional analysis is the study of vector spaces of arbitrary dimension over the field of real or complex numbers, and the continuous linear mappings between such spaces. Naturally, the notion of continuity requires a…
A highly comparative, feature-based approach to time series classification is introduced that uses an extensive database of algorithms to extract thousands of interpretable features from time series. These features are derived from across…
In this review, we present some fundamental classical and quantum phenomena in view of time fractional formalism. Time fractional formalism is a very useful tool in describing systems with memory and delay. We hope that this study can…
In this paper we address the problem of feature selection when the data is functional, we study several statistical procedures including classification, regression and principal components. One advantage of the blinding procedure is that it…
These lecture notes provide an overview of existing methodologies and recent developments for estimation and inference with high dimensional time series regression models. First, we present main limit theory results for high dimensional…
Large tensor (multi-dimensional array) data are now routinely collected in a wide range of applications, due to modern data collection capabilities. Often such observations are taken over time, forming tensor time series. In this paper we…
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…
In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…
Motivated by the need to statistically quantify differences between modern (complex) data-sets which commonly result as high-resolution measurements of stochastic processes varying over a continuum, we propose novel testing procedures to…
Multivariate time series classification is a task with increasing importance due to the proliferation of new problems in various fields (economy, health, energy, transport, crops, etc.) where a large number of information sources are…
Functional data analysis, which handles data arising from curves, surfaces, volumes, manifolds and beyond in a variety of scientific fields, is a rapidly developing area in modern statistics and data science in the recent decades. The…
A characteristic feature of functional data is the presence of phase variability in addition to amplitude variability. Existing functional regression methods do not handle time variability in an explicit and efficient way. In this paper we…