Related papers: Wavelet-based and Fourier-based multivariate Whitt…
In this paper we present a multiresolution-based method for period determination that is able to deal with unevenly sampled data. This method allows us to detect superimposed periodic signals with lower signal-to-noise ratios than in…
Time series data analysis is a critical component in various domains such as finance, healthcare, and meteorology. Despite the progress in deep learning for time series analysis, there remains a challenge in addressing the non-stationary…
Many scientific areas, from computer science to the environmental sciences and finance, give rise to multivariate time series which exhibit long memory, or loosely put, a slow decay in their autocorrelation structure. Efficient modelling…
Full-waveform inversion (FWI) is an advanced technique for reconstructing high-resolution subsurface physical parameters by progressively minimizing the discrepancy between observed and predicted seismic data. However, conventional FWI…
Brownian motion and fractional Brownian motion have been widely applied in statistical modeling in finance, telecommunication, network traffic, neuroscience, physics, and other fields. More realistic models for real time series data, such…
Experiments in many fields of science and engineering yield data in the form of time series. The Fourier and wavelet transform-based nonparametric methods are used widely to study the spectral characteristics of these time series data.…
The empirical wavelet transform is an adaptive multiresolution analysis tool based on the idea of building filters on a data-driven partition of the Fourier domain. However, existing 2D extensions are constrained by the shape of the…
Time-frequency representations (TFRs) of signals, such as the windowed Fourier transform (WFT), wavelet transform (WT) and their synchrosqueezed variants (SWFT, SWT), provide powerful analysis tools. However, there are many important issues…
We propose a numerical algorithm for backward stochastic differential equations based on time discretization and trigonometric wavelets. This method combines the effectiveness of Fourier-based methods and the simplicity of a wavelet-based…
In this paper we estimate the dynamic parameters of a time-varying coefficient model through radial kernel functions in the context of a longitudinal study. Our proposal is based on a linear combination of weighted kernel functions…
We present the Mathematica package MultivariateResidues, which allows for the efficient evaluation of multivariate residues based on methods from computational algebraic geometry. Multivariate residues appear in several contexts of…
Multi-time wave functions are wave functions for multi-particle quantum systems that involve several time variables (one per particle). In this paper we contrast them with solutions of wave equations on a space-time with multiple timelike…
Time delay estimation plays a critical role in control, stabilization and state estimation of many practical system with time delay. In this paper, we propose a method to estimate delay for discrete time linear multiple-input…
We revisit the use of spectral techniques to replaces the attention mechanism in Transformers through Fourier Transform based token mixing, and present a comprehensive and novel reformulation of this technique in next generation transformer…
A wavelet-based method for compression of three-dimensional simulation data is presented and its software framework is described. It uses wavelet decomposition and subsequent range coding with quantization suitable for floating-point data.…
We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet…
Most time series observed in practice exhibit time-varying trend (first-order) and autocovariance (second-order) behaviour. Differencing is a commonly-used technique to remove the trend in such series, in order to estimate the time-varying…
Multivariate time series classification is an important computational task arising in applications where data is recorded over time and over multiple channels. For example, a smartwatch can record the acceleration and orientation of a…
This paper proposes Fourier-based and wavelet-based techniques for analyzing periodic financial time series. Conventional models such as the periodic autoregressive conditional heteroscedastic (PGARCH) and periodic autoregressive…
Researchers have used many different methods to detect the possibility of long-term dependence (long memory) in stock market returns, but evidence is in general mixed. In this paper, three different tests, (namely Rescaled Range (R/S), its…