Related papers: Functional Time Series Analysis Based on Records
Topological Data Analysis (TDA) is a rising field of computational topology in which the topological structure of a data set can be observed by persistent homology. By considering a sequence of sublevel sets, one obtains a filtration that…
Time series analysis is crucial for understanding dynamics of complex systems. Recent advances in foundation models have led to task-agnostic Time Series Foundation Models (TSFMs) and Large Language Model-based Time Series Models (TSLLMs),…
Functional data analysis is concerned with the analysis of infinite-dimensional data functions. Functional principal component analysis (FPCA) is a key method to obtain finite-dimensional summaries. Consistency of FPCA has been…
Over the last few years, with the growth of time-series collecting and storing, there has been a great demand for tools and software for temporal data engineering and modeling. This paper presents a generic workflow for time series data…
Statistical analysis of high-dimensional functional times series arises in various applications. Under this scenario, in addition to the intrinsic infinite-dimensionality of functional data, the number of functional variables can grow with…
The paper introduces a general framework for statistical analysis of functional time series from a Bayesian perspective. The proposed approach, based on an extension of the popular dynamic linear model to Banach-space valued observations…
The internal state of a dynamical system, a set of variables that defines its evolving configuration, is often hidden and cannot be fully measured, posing a central challenge for real-time monitoring and control. While observers are…
Functional depth is the functional data analysis technique that orders a functional data set. Unlike the case of data on the real line, defining this order is non-trivial, and particularly, with functional data, there are a number of…
Detecting anomalies and the corresponding root causes in multivariate time series plays an important role in monitoring the behaviors of various real-world systems, e.g., IT system operations or manufacturing industry. Previous anomaly…
Ordinal time series analysis is based on the idea to map time series to ordinal patterns, i.e., order relations between the values of a time series and not the values themselves, as introduced in 2002 by C. Bandt and B. Pompe. Despite a…
Estimations and evaluations of the main patterns of time series data in groups benefit large amounts of applications in various fields. Different from the classical auto-correlation time series analysis and the modern neural networks…
The Fourier phase information play a key role for the quantified description of nonlinear data. We present a novel tool for time series analysis that identifies nonlinearities by sensitively detecting correlations among the Fourier phases.…
Topological data analysis (TDA) is a versatile tool that can be used to extract scientific knowledge from complex pattern formation processes. However, the physics correspondence between the features obtained from TDA and pattern dynamics…
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…
In the functional linear regression model, many methods have been proposed and studied to estimate the slope function while the functional predictor was observed in the entire domain. However, works on functional linear regression models…
Functional concurrent, or varying-coefficient, regression models are commonly used in biomedical and clinical settings to investigate how the relation between an outcome and observed covariate varies as a function of another covariate. In…
For the purpose of monitoring the behavior of complex infrastructures (e.g. aircrafts, transport or energy networks), high-rate sensors are deployed to capture multivariate data, generally unlabeled, in quasi continuous-time to detect…
We propose nonparametric methods for functional linear regression which are designed for sparse longitudinal data, where both the predictor and response are functions of a covariate such as time. Predictor and response processes have smooth…
We introduce FDApy, an open-source Python package for the analysis of functional data. The package provides tools for the representation of (multivariate) functional data defined on different dimensional domains and for functional data that…
Exploratory Data Analysis (EDA) is a routine task for data analysts, often conducted using flexible computational notebooks. During EDA, data workers process, visualize, and interpret data tables, making decisions about subsequent analysis.…