Related papers: Functional Time Series
Time series are ubiquitous in our data rich world. In what follows I will describe how ideas from dynamical systems and topological data analysis can be combined to gain insights from time-varying data. We will see several applications to…
The goal of data-driven learning of dynamical systems is to interpret time series as a continuous observation of an underlying dynamical system. This task is not well-posed for a variety of reasons - such as multiple co-existing…
Within the framework of functional data analysis, we develop principal component analysis for periodically correlated time series of functions. We define the components of the above analysis including periodic, operator-valued filters,…
Due to the huge progress of the recording devices, data from heterogeneous nature can be recorded, such as spatial, temporal and spatio-temporal. Nowadays, time-based data is of particular interest since it has the ability to capture the…
Cosmic demographics -- the statistical study of populations of astrophysical objects -- has long relied on *multivariate statistics*, providing methods for analyzing data comprising fixed-length vectors of properties of objects, as might be…
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…
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…
With the rise of Industry 4.0, huge amounts of data are now generated that are apt to be modelled as functional data. In this setting, standard profile monitoring methods aim to assess the stability over time of a completely observed…
Time series analysis is a field of data science which is interested in analyzing sequences of numerical values ordered in time. Time series are particularly interesting because they allow us to visualize and understand the evolution of a…
Time series are all around in real-world applications. However, unexpected accidents for example broken sensors or missing of the signals will cause missing values in time series, making the data hard to be utilized. It then does harm to…
Aggregation of large databases in a specific format is a frequently used process to make the data easily manageable. Interval-valued data is one of the data types that is generated by such an aggregation process. Using traditional methods…
Time-series analysis is fundamental for modeling and predicting dynamical behaviors from time-ordered data, with applications in many disciplines such as physics, biology, finance, and engineering. Measured time-series data, however, are…
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.…
Topological data analysis (TDA), while abstract, allows a characterization of time-series data obtained from nonlinear and complex dynamical systems. Though it is surprising that such an abstract measure of structure - counting pieces and…
The continued digitization of societal processes translates into a proliferation of time series data that cover applications such as fraud detection, intrusion detection, and energy management, where anomaly detection is often essential to…
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…
This paper explores the application of functional data analysis (FDA) as a means to study the dynamics of software evolution in the open source context. Several challenges in analyzing the data from software projects are discussed, an…
Improvements in data acquisition and processing techniques have lead to an almost continuous flow of information for financial data. High resolution tick data are available and can be quite conveniently described by a continuous time…
Time series data are prevalent across various domains and often encompass large datasets containing multiple time-dependent features in each sample. Exploring time-varying data is critical for data science practitioners aiming to understand…
Interest in functional time series has spiked in the recent past with papers covering both methodology and applications being published at a much increased pace. This article contributes to the research in this area by proposing a new…