相关论文: Discriminant Analysis in stationary time series ba…

Progress on modern scientific questions regularly depends on using large-scale datasets to understand complex dynamical systems. An especially challenging case that has grown to prominence with advances in single-cell sequencing…

We introduce a statistical method to detect nonlinearity and nonstationarity in time series, that works even for short sequences and in presence of noise. The method has a discrimination power similar to that of the most advanced estimators…

In a number of data-driven applications such as detection of arrhythmia, interferometry or audio compression, observations are acquired indistinctly in the time or frequency domains: temporal observations allow us to study the spectral…

Current approaches for time series forecasting, whether in the time or frequency domain, predominantly use deep learning models based on linear layers or transformers. They often encode time series data in a black-box manner and rely on…

Time series forecasting faces two important but often overlooked challenges. Firstly, the inherent random noise in the time series labels sets a theoretical lower bound for the forecasting error, which is positively correlated with the…

Many real-world systems modeled using differential equations involve unknown or uncertain parameters. Standard approaches to address parameter estimation inverse problems in this setting typically focus on estimating constants; yet some…

Regularized linear discriminant analysis (RLDA) is a widely used tool for classification and dimensionality reduction, but its performance in high-dimensional scenarios is inconsistent. Existing theoretical analyses of RLDA often lack clear…

We present an end-to-end differentiable neural network architecture to perform anomaly detection in multivariate time series by incorporating a Sequential Probability Ratio Test on the prediction residual. The architecture is a cascade of…

In this paper we propose a scalable version of a state-of-the-art deterministic time-invariant feature extraction approach based on consecutive changes of basis and nonlinearities, namely, the scattering network. The first focus of the…

Accurate time series analysis is essential for studying variable astronomical sources, where detecting periodicities and characterizing power spectral density (PSD) are crucial. The Lomb-Scargle periodogram, commonly used in astronomy for…

Cyclic spectral analysis is a signal processing technique designed to deal with stochastic signals whose statistics vary periodically with time. Pulsar radio emission is a textbook example of this signal class, known as cyclostationary…

Time series forecasting models are becoming increasingly prevalent due to their critical role in decision-making across various domains. However, most existing approaches represent the coupled temporal patterns, often neglecting the…

An important feature of all real-world networks is that the network structure changes over time. Due to this dynamic nature, it becomes difficult to propose suitable growth models that can explain the various important characteristic…

This article considers a nonparametric method for detecting change points in non-stationary time series. The proposed method will divide the time series into several segments so that between two adjacent segments, the normalized spectral…

Although classical spectral analysis is a natural approach to characterise linear systems, it cannot describe a chaotic dynamics. Here, we propose the ordinal spectrum, a method based on a spectral transformation of symbolic sequences, to…

Classical spectral methods are subject to two fundamental limitations: they only can account for covariance-related serial dependencies, and they require second-order stationarity. Much attention has been devoted lately to quantile-based…

This paper presents \textbf{FreEformer}, a simple yet effective model that leverages a \textbf{Fre}quency \textbf{E}nhanced Trans\textbf{former} for multivariate time series forecasting. Our work is based on the assumption that the…

Quadratic discriminant analysis (QDA) is a widely used classification technique that generalizes the linear discriminant analysis (LDA) classifier to the case of distinct covariance matrices among classes. For the QDA classifier to yield…

Method for detection and visualization of trends, periodicities, local peculiarities in measurement series (dL-method) based on DFA technology (Detrended fluctuation analysis) is proposed. The essence of the method lies in reflecting the…

In this paper, we present an assortment of both standard and advanced Fourier techniques that are useful in the analysis of astrophysical time series of very long duration -- where the observation time is much greater than the time…