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We develop a new method to find the number of volatility regimes in a nonstationary financial time series by applying unsupervised learning to its volatility structure. We use change point detection to partition a time series into locally…
Multiscale phenomena that evolve on multiple distinct timescales are prevalent throughout the sciences. It is often the case that the governing equations of the persistent and approximately periodic fast scales are prescribed, while the…
This paper proposes a hierarchical approximate-factor approach to analyzing high-dimensional, large-scale heterogeneous time series data using distributed computing. The new method employs a multiple-fold dimension reduction procedure using…
We propose a novel approach to the problem of clustering hierarchically aggregated time-series data, which has remained an understudied problem though it has several commercial applications. We first group time series at each aggregated…
Temporal event data are collected across a broad range of domains, and a variety of visual analytics techniques have been developed to empower analysts working with this form of data. These techniques generally display aggregate statistics…
Clustering techniques are very attractive for extracting and identifying patterns in datasets. However, their application to very large spatial datasets presents numerous challenges such as high-dimensionality data, heterogeneity, and high…
Different methods are used to determine the scaling exponents associated with a time series describing a complex dynamical process, such as those observed in geophysical systems. Many of these methods are based on the numerical evaluation…
Our understanding of a variety of phenomena in physics, biology and economics crucially depends on the analysis of multivariate time series. While a wide range of tools and techniques for time series analysis already exist, the increasing…
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…
Clustering procedures suitable for the analysis of very high-dimensional data are needed for many modern data sets. In model-based clustering, a method called high-dimensional data clustering (HDDC) uses a family of Gaussian mixture models…
In several environmental applications data are functions of time, essentially con- tinuous, observed and recorded discretely, and spatially correlated. Most of the methods for analyzing such data are extensions of spatial statistical tools…
We formulate a novel technique for the detection of functional clusters in discrete event data. The advantage of this algorithm is that no prior knowledge of the number of functional groups is needed, as our procedure progressively combines…
Clustering is an essential technique for discovering patterns in data. The steady increase in amount and complexity of data over the years led to improvements and development of new clustering algorithms. However, algorithms that can…
In multivariate time series systems, key insights can be obtained by discovering lead-lag relationships inherent in the data, which refer to the dependence between two time series shifted in time relative to one another, and which can be…
In this paper, we set up the theoretical foundations for a high-dimensional functional factor model approach in the analysis of large cross-sections (panels) of functional time series (FTS). We first establish a representation result…
The dynamical evolution of multiscaling in financial time series is investigated using time-dependent Generalized Hurst Exponents (GHE), $H_q$, for various values of the parameter $q$. Using $H_q$, we introduce a new visual methodology to…
The unsupervised and principled diagnosis of multi-scale data is a fundamental obstacle in modern scientific problems from, for instance, weather and climate prediction, neurology, epidemiology, and turbulence. Multi-scale data is…
Multi-step forecasting (MSF) in time-series, the ability to make predictions multiple time steps into the future, is fundamental to almost all temporal domains. To make such forecasts, one must assume the recursive complexity of the…
Large-scale multiple testing under static factor models is widely used to detect sparse signals in high-dimensional data. However, static factor models are arguably too stringent because they ignore serial correlation, which seriously…
Multivariate time series forecasting is crucial across various industries, where accurate extraction of complex periodic and trend components can significantly enhance prediction performance. However, existing models often struggle to…