Related papers: Fast Time Series Detrending with Applications to H…

Multivariate time-series have become abundant in recent years, as many data-acquisition systems record information through multiple sensors simultaneously. In this paper, we assume the variables pertain to some geometry and present an…

This paper establishes the convergence of a time-steeping scheme for time fractional diffusion problems with nonsmooth data. We first analyze the regularity of the model problem with nonsmooth data, and then prove that the time-steeping…

This paper presents a nonlinear reaction-diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions,…

Detrended fluctuation analysis (DFA) and detrended moving average (DMA) are two scaling analysis methods designed to quantify correlations in noisy non-stationary signals. We systematically study the performance of different variants of the…

We study time series concerning rare events. The occurrence of a rare event is depicted as a jump of constant intensity always occurring in the same direction, thereby generating an asymmetric diffusion process. We consider the case where…

Singular spectrum analysis (SSA) as a nonparametric tool for decomposition of an observed time series into sum of interpretable components such as trend, oscillations and noise is considered. The separability of these series components by…

Time series prediction covers a vast field of every-day statistical applications in medical, environmental and economic domains. In this paper we develop nonparametric prediction strategies based on the combination of a set of 'experts' and…

A useful approach for analysing multiple time series is via characterising their spectral density matrix as the frequency domain analog of the covariance matrix. When the dimension of the time series is large compared to their length,…

Piecewise Aggregate Approximation (PAA) is a competitive basic dimension reduction method for high-dimensional time series mining. When deployed, however, the limitations are obvious that some important information will be missed,…

Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results…

Signal decomposition and multiscale signal analysis provide many useful tools for time-frequency analysis. We proposed a random feature method for analyzing time-series data by constructing a sparse approximation to the spectrogram. The…

Multivariate Singular Spectrum Analysis (MSSA) is a powerful and widely used nonparametric method for multivariate time series, which allows the analysis of complex temporal data from diverse fields such as finance, healthcare, ecology, and…

Statistical static timing analysis deals with the increasing variations in manufacturing processes to reduce the pessimism in the worst case timing analysis. Because of the correlation between delays of circuit components, timing model…

We present a new framework for robust estimation and inference on second-order stationary time series and random fields. This framework is based on the Generalized Method of Wavelet Moments which uses the wavelet variance to achieve…

Particle Image Velocimetry (PIV) has become increasingly popular to study structures in turbulent flows. PIV allows direct extraction and investigation of spatial structures in the given flow field. Increasing temporal resolution of PIV…

This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…

Adapting pretrained diffusion models to downstream objectives such as inverse problems often requires expensive test-time guidance or optimization. We propose a principled framework for generating high-quality reward-aligned samples at…

The non-stationary evolution of observable quantities in complex systems can frequently be described as a juxtaposition of quasi-stationary spells. Given that standard theoretical and data analysis approaches usually rely on the assumption…

This paper presents a practical approach for detecting non-stationarity in time series prediction. This method is called SAFE and works by monitoring the evolution of the spectral contents of time series through a distance function. This…

For the classical reaction diffusion equation, the priori speed of fronts is determined exactly in the pioneering paper (R.D. Benguria and M.C. Depassier, {\em Commun. Math. Phys.} 175:221--227, 1996) by variational characterization method.…