Related papers: Weakly dependent functional data
Functional data analysis offers a diverse toolkit of statistical methods tailored for analyzing samples of real-valued random functions. Recently, samples of time-varying random objects, such as time-varying networks, have been increasingly…
In many phenomena, data are collected on a large scale and of different frequencies. In this context, functional data analysis (FDA) has become an important statistical methodology for analyzing and modeling such data. The approach of FDA…
The literature on time series of functional data has focused on processes of which the probabilistic law is either constant over time or constant up to its second-order structure. Especially for long stretches of data it is desirable to be…
Modeling functions that are sequentially observed as functional time series is becoming increasingly common. In such models, it is often crucial to ensure data homogeneity. We investigate the sensitivity of graph-based change point…
High dimensional time series datasets are becoming increasingly common in various fields such as economics, finance, meteorology, and neuroscience. Given this ubiquity of time series data, it is surprising that very few works on variable…
We consider the estimation of large covariance and precision matrices from high-dimensional sub-Gaussian or heavier-tailed observations with slowly decaying temporal dependence. The temporal dependence is allowed to be long-range so with…
Functional principal component analysis has been shown to be invaluable for revealing variation modes of longitudinal outcomes, which serves as important building blocks for forecasting and model building. Decades of research have advanced…
Identifying relationships among stochastic processes is a core objective in many fields, such as economics. While the standard toolkit for multivariate time series analysis has many advantages, it can be difficult to capture nonlinear…
Recent technological developments have enabled us to collect complex and high-dimensional data in many scientific fields, such as population health, meteorology, econometrics, geology, and psychology. It is common to encounter such datasets…
Assessing the predictive power of both data and models holds paramount significance in time-series machine learning applications. Yet, preparing time series data accurately and employing an appropriate measure for predictive power seems to…
Functional magnetic resonance imaging (fMRI) data provides information concerning activity in the brain and in particular the interactions between brain regions. Resting state fMRI data is widely used for inferring connectivities in the…
Time series data is a collection of chronological observations which is generated by several domains such as medical and financial fields. Over the years, different tasks such as classification, forecasting, and clustering have been…
Spatio-temporal covariances are important for describing the spatio-temporal variability of underlying random processes in geostatistical data. For second-order stationary processes, there exist subclasses of covariance functions that…
Functional data is a powerful tool for capturing and analyzing complex patterns and relationships in a variety of fields, allowing for more precise modeling, visualization, and decision-making. For example, in healthcare, functional data…
The paper studies the asymptotic behaviour of weighted functionals of long-range dependent data over increasing observation windows. Various important statistics, including sample means, high order moments, occupation measures can be given…
The paper deals with variational approaches to the segmentation of time series into smooth pieces, but allowing for sharp breaks. In discrete time, the corresponding functionals are of Blake-Zisserman type. Their natural counterpart in…
We develop a testing procedure for distinguishing between a long-range dependent time series and a weakly dependent time series with change-points in the mean. In the simplest case, under the null hypothesis the time series is weakly…
A functional limit theorem is established for the partial-sum process of a class of stationary sequences which exhibit both heavy tails and long-range dependence. The stationary sequence is constructed using multiple stochastic integrals…
In this paper, we propose two nonparametric methods used in the forecasting of functional time-dependent data, namely functional singular spectrum analysis recurrent forecasting and vector forecasting. Both algorithms utilize the results of…
Many analyses of functional magnetic resonance imaging (fMRI) examine functional connectivity (FC), or the statistical dependencies among distant brain regions. These analyses are typically exploratory, guiding future confirmatory research.…