Related papers: Asymmetric Huber Periodogram
Monitoring complex systems results in massive multivariate time series data, and anomaly detection of these data is very important to maintain the normal operation of the systems. Despite the recent emergence of a large number of anomaly…
A hybrid estimator of the log-spectral density of a stationary time series is proposed. First, a multiple taper estimate is performed, followed by kernel smoothing the log-multitaper estimate. This procedure reduces the expected mean square…
The least-squares (or Lomb-Scargle) periodogram is a powerful tool which is used routinely in many branches of astronomy to search for periodicities in observational data. The problem of assessing statistical significance of candidate…
The detection and characterization of quantum coherence is of fundamental importance both in the foundations of quantum theory as well as for the rapidly developing field of quantum technologies, where coherence has been linked to quantum…
In Patil et. al 2024a, we developed a multitaper power spectrum estimation method, mtNUFFT, for analyzing time-series with quasi-regular spacing, and showed that it not only improves upon the statistical issues of the Lomb-Scargle…
In this work a detailed spectral analysis of the time series of the 8B solar neutrino flux published by the Super-Kamiokande Collaboration is presented, performed through a likelihood scan approach. Preliminarily a careful review of the…
In multivariate time series (MTS) forecasting, many deep learning based methods have been proposed for modeling dependencies at multiple spatial (inter-variate) or temporal (intra-variate) scales. However, existing methods may fail to model…
Traditional pairwise sequence alignment is based on matching individual samples from two sequences, under time monotonicity constraints. However, in many application settings matching subsequences (segments) instead of individual samples…
The Homotopy Analysis Method (HAM) is a widely used analytical approach for solving nonlinear problems, yet its theoretical foundation lacks rigorous justification, and its intrinsic correlation with perturbation theory remains ambiguous,…
Despite the population of the noninvasive, economic, comfortable, and easy-to-install photoplethysmography (PPG), it is still lacking a mathematically rigorous and stable algorithm which is able to simultaneously extract from a…
Wearable photoplethysmography (WPPG) has recently become a common technology in heart rate (HR) monitoring. General observation is that the motion artifacts change the statistics of the acquired PPG signal. Consequently, estimation of HR…
Many speech and music analysis and processing schemes rely on an estimate of the fundamental frequency $f_0$ of periodic signal components. Most established schemes apply rather unspecific signal models such as sinusoidal models to the…
Multivariate time series analysis is a vital but challenging task, with multidisciplinary applicability, tackling the characterization of multiple interconnected variables over time and their dependencies. Traditional methodologies often…
A new class of measurement operators, coined hierarchical measurement operators, and prove results guaranteeing the efficient, stable and robust recovery of hierarchically structured signals from such measurements. We derive bounds on their…
Astrophysical time series often contain periodic signals. The large and growing volume of time series data from photometric surveys demands computationally efficient methods for detecting and characterizing such signals. The most efficient…
The horizontal visibility algorithm has been recently introduced as a mapping between time series and networks. The challenge lies in characterizing the structure of time series (and the processes that generated those series) using the…
Supermassive black hole binary (SMBHB) systems are expected to form as a consequence of galaxy mergers. At sub-parsec separations, SMBHBs can be identified as quasars with periodic variability with previous periodicity searches uncovering…
High harmonic generation (HHG) is used to measure the spectral phase of the recombination dipole matrix element (RDM) in argon over a broad frequency range that includes the 3p Cooper minimum (CM). The measured RDM phase agrees well with…
While the Lomb-Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60-year history of developing…
Anomaly detection on multivariate time-series is of great importance in both data mining research and industrial applications. Recent approaches have achieved significant progress in this topic, but there is remaining limitations. One major…