Related papers: Multivariate Fractional Components Analysis
The importance of fractional time-derivative to take care of memory effects has been brought out by considering the example of a simple oscillator.
This paper is devoted to the study of the flatness property of linear time-invariant fractional systems. In the framework of polynomial matrices of the fractional derivative operator, we give a characterization of fractionally flat outputs…
Multivariate spatio-temporal data arise more and more frequently in a wide range of applications; however, there are relatively few general statistical methods that can readily use that incorporate spatial, temporal and variable…
Analyzing multivariate time series data is important to predict future events and changes of complex systems in finance, manufacturing, and administrative decisions. The expressiveness power of Gaussian Process (GP) regression methods has…
In this study, a longitudinal regression model for covariance matrix outcomes is introduced. The proposal considers a multilevel generalized linear model for regressing covariance matrices on (time-varying) predictors. This model…
Functional magnetic resonance imaging (fMRI) data contain complex spatiotemporal dynamics, thus researchers have developed approaches that reduce the dimensionality of the signal while extracting relevant and interpretable dynamics. Models…
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…
Nonlinear thermoelastic systems play a crucial role in understanding thermal conductivity, stresses, elasticity, and temperature interactions. This research focuses on finding solutions to these systems in their fractional forms, which is a…
In mixed longitudinal studies, a group of subjects enter the study at different ages (cross-sectional) and are followed for successive years (longitudinal). In the context of such studies, we consider nonparametric covariance estimation…
We consider the estimation of approximate factor models for time series data, where strong serial and cross-sectional correlations amongst the idiosyncratic component are present. This setting comes up naturally in many applications, but…
A considerable amount of clustering algorithms take instance-feature matrices as their inputs. As such, they cannot directly analyze time series data due to its temporal nature, usually unequal lengths, and complex properties. This is a…
The simulation of systems that act on multiple time scales is challenging. A stable integration of the fast dynamics requires a highly accurate approximation whereas for the simulation of the slow part, a coarser approximation is accurate…
In this paper, a nonlinear system of fractional ordinary differential equations with multiple scales in time is investigated. We are interested in the effective long-term computation of the solution. The main challenge is how to obtain the…
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…
The study of systems with memory requires methods which are different from the methods used in regular dynamics. Systems with power-law memory in many cases can be described by fractional differential equations, which are…
A full parametric and linear specification may be insufficient to capture complicated patterns in studies exploring complex features, such as those investigating age-related changes in brain functional abilities. Alternatively, a partially…
Multivariate functional data present theoretical and practical complications which are not found in univariate functional data. One of these is a situation where the component functions of multivariate functional data are positive and are…
We introduce an efficient variational hybrid quantum-classical algorithm designed for solving Caputo time-fractional partial differential equations. Our method employs an iterable cost function incorporating a linear combination of overlap…
We obtain invariance principles for a wide class of fractionally integrated nonlinear processes. The limiting distributions are shown to be fractional Brownian motions. Under very mild conditions, we extend earlier ones on long memory…
We develop a generalization of unobserved components models that allows for a wide range of long-run dynamics by modelling the permanent component as a fractionally integrated process. The model does not require stationarity and can be cast…