Related papers: Detecting a Structural Change in Functional Time S…
This paper describes opportunities and challenges of using functional data analysis (FDA) for the exploration and analysis of data originating from electronic commerce (eCommerce). We discuss the special data structures that arise in the…
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…
Functional Principal Components Analysis (FPCA) is a widely used analytic tool for dimension reduction of functional data. Traditional implementations of FPCA estimate the principal components from the data, then treat these estimates as…
Recent results in coupled or temporal graphical models offer schemes for estimating the relationship structure between features when the data come from related (but distinct) longitudinal sources. A novel application of these ideas is for…
Multivariate functional principal component analysis (MFPCA) is a powerful dimension reduction technique for analyzing multiple functional variables simultaneously. However, existing MFPCA methods assume that all functional observations are…
Frequently econometricians are interested in verifying a relationship between two or more time series. Such analysis is typically carried out by causality and/or independence tests which have been well studied when the data is univariate or…
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…
We consider inference problems for high-dimensional (HD) functional data with a dense number (T) of repeated measurements taken for a large number of p variables from a small number of n experimental units. The spatial and temporal…
The abundance of functional observations in scientific endeavors has led to a significant development in tools for functional data analysis (FDA). This kind of data comes with several challenges: infinite-dimensionality of function spaces,…
We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in…
This work proposes and study the concept of Functional Data Analysis transform, applying it to the performance improving of volumetric Bouligand-Minkowski fractal descriptors. The proposed transform consists essentially in changing the…
Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation…
As the development of measuring instruments and computers has accelerated the collection of massive amounts of data, functional data analysis (FDA) has experienced a surge of attention. The FDA methodology treats longitudinal data as a set…
Sparse functional data arise when measurements are observed infrequently and at irregular time points for each subject, often in the presence of measurement error. These characteristics introduce additional challenges for functional…
Multifractal detrended fluctuation analysis (MFDFA) has become a central method to characterise the variability and uncertainty in empiric time series. Extracting the fluctuations on different temporal scales allows quantifying the strength…
The study of topology is strictly speaking, a topic in pure mathematics. However in only a few years, Topological Data Analysis (TDA), which refers to methods of utilizing topological features in data (such as connected components, tunnels,…
In many modern applications, a dependent functional response is observed for each subject over repeated time, leading to longitudinal functional data. In this paper, we propose a novel statistical procedure to test whether the mean function…
An important issue in functional time series analysis is whether an observed series comes from a purely random process. We extend the BDS test, a widely-used nonlinear independence test, to the functional time series. Like the BDS test in…
Analyzing time series in the frequency domain enables the development of powerful tools for investigating the second-order characteristics of multivariate processes. Parameters like the spectral density matrix and its inverse, the coherence…
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…