Related papers: Functional Time Series Analysis Based on Records
We develop theory leading to testing procedures for the presence of a change point in the intraday volatility pattern. The new theory is developed in the framework of Functional Data Analysis. It is based on a model akin to the stochastic…
The quantitative understanding and precise control of complex dynamical systems can only be achieved by observing their internal states via measurement and/or estimation. In large-scale dynamical networks, it is often difficult or…
Functional data analysis is ubiquitous in most areas of sciences and engineering. Several paradigms are proposed to deal with the dimensionality problem which is inherent to this type of data. Sparseness, penalization, thresholding, among…
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…
Time series analysis has proven to be a powerful method to characterize several phenomena in biology, neuroscience and economics, and to understand some of their underlying dynamical features. Despite a plethora of methods have been…
Many fMRI analyses examine functional connectivity, or statistical dependencies among remote brain regions. Yet popular methods for studying whole-brain functional connectivity often yield results that are difficult to interpret. Factor…
Performance monitoring, anomaly detection, and root-cause analysis in complex cyber-physical systems (CPSs) are often highly intractable due to widely diverse operational modes, disparate data types, and complex fault propagation…
We study statistical inference on unit roots and cointegration for time series in a Hilbert space. We develop statistical inference on the number of common stochastic trends embedded in the time series, i.e., the dimension of the…
Analyzing longitudinal data in health studies is challenging due to sparse and error-prone measurements, strong within-individual correlation, missing data and various trajectory shapes. While mixed-effect models (MM) effectively address…
Nowadays data sets are available in very complex and heterogeneous ways. Mining of such data collections is essential to support many real-world applications ranging from healthcare to marketing. In this work, we focus on the analysis of…
Finding parametric models that accurately describe the dependence structure of observed data is a central task in the analysis of time series. Classical frequency domain methods provide a popular set of tools for fitting and diagnostics of…
Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…
We present a Bayesian approach for modeling multivariate, dependent functional data. To account for the three dominant structural features in the data--functional, time dependent, and multivariate components--we extend hierarchical dynamic…
In recent years, manifold methods have moved into focus as tools for dimension reduction. Assuming that the high-dimensional data actually lie on or close to a low-dimensional nonlinear manifold, these methods have shown convincing results…
Control charts for process monitoring are widely used in practice. Most control charts require the monitored (residuals) process to be serially independent (and to satisfy specified distributional assumptions), whereas undetected dependence…
Based on the well-known Detrended Fluctuation Analysis (DFA) for time series, in this work we describe a DFA for continuous real variable functions. Under certain conditions, DFA accurately predicts the long-term auto-correlation of the…
Recent developments in big data analysis, machine learning, Industry 4.0, and IoT applications have enabled the monitoring and processing of multi-sensor data collected from systems, allowing for the prediction of the "Remaining Useful…
This article presents an Analysis of Variance model for functional data that explicitly incorporates phase variability through a time-warping component, allowing for a unified approach to estimation and inference in presence of amplitude…
A time series represents a set of observations collected over time. Typically, these observations are captured with a uniform sampling frequency (e.g. daily). When data points are observed in uneven time intervals the time series is…
Irregularly sampled time series with missing values are often observed in multiple real-world applications such as healthcare, climate and astronomy. They pose a significant challenge to standard deep learning models that operate only on…