Paper proposes a forecasting model combining autoregressive models with spectral attention.
problem Time series forecasting across various domains.
method Combines deep autoregressive models with Spectral Attention (SA) module.
result SAAM consistently demonstrates improved forecasting accuracy compared to state-of-the-art approaches.
Robust clustering for time series using spectral densities and functional data analysis.
problem Clustering stationary time series data robustly.
method Spectral densities as functional data, robust clustering algorithm applied, trimming and restrictions used.
result Reduction of noise and prevention of spurious clusters.
Paper develops a method for estimating spectral density matrices in high-dimensional time series.
problem Estimating spectral density matrices in high-dimensional time series.
method Thresholded versions of averaged periodograms for regularized estimation.
result Consistent estimation of spectral density matrices possible under high-dimensional regime.
Spectral Independence Criterion helps infer cause-effect relationships in time series.
problem Distinguishing cause from effect in time series data.
method Spectral Independence Criterion (SIC) based on PSD and frequency response.
result SIC provides a robust method for causal inference in time series data.
Introduces Spectral Attention for better long-range time series forecasting.
problem Challenges in capturing long-range dependencies in time series forecasting.
method Spectral Attention mechanism that preserves temporal correlations and long-range dependencies.
result Achieves state-of-the-art results on 11 real-world time series datasets.
Meta-learning for Koopman spectral analysis with short time-series data.
problem Lack of long time-series for training embedding functions in Koopman spectral analysis.
method Meta-learning approach using bidirectional LSTM and neural network to estimate embedding functions from short time-series.
result The proposed method achieves better performance in eigenvalue estimation and future prediction compared to existing methods.
Unified framework for generating meteorological time series from text.
problem Lack of large-scale, physically grounded multimodal datasets and architectures ignoring spectral-temporal structure.
method Introduce MeteoCap-3B dataset and MTransformer model.
result State-of-the-art generation quality, accurate cross-modal alignment, strong semantic controllability.
Bayesian method models financial time series with non-stationarity and dependency.
problem Discrimination between non-stationarity and long-range dependency in financial time series.
method Adaptive spectral technique using non-parametric Bayesian inference with Reversible Jump Markov Chain Monte Carlo.
result Bayesian method effectively models both long-range dependency and non-stationarity in financial time series.
New framework detects directional influence in multivariate time series.
problem Detecting directional influence in multivariate time series.
method Order-constrained spectral non-invariance.
result Unique diagnostic functional for directional influence.
Proposes a parsimonious graph spectral method for time series data.
problem Efficiently transmitting multivariate time series data.
method Graph spectral embedding with unsupervised, parsimonious encoding.
result Near-linear computational complexity and interpretable event structure.
Improved algorithm for learning OOMs from time series with missing data.
problem Handling missing data in time series models with non-independent missingness patterns.
method Refined spectral OOM learning algorithm for time series with missing values, proving consistency under relaxed conditions.
result The refined algorithm can consistently handle complex missingness patterns interacting with the visible process.
Deep learning speeds spectral density estimation for large 2D/3D grids.
problem Computational challenges in estimating spectral densities for large grids.
method Deep learning neural network for spectral density estimation.
result Deep learning estimator is a universal approximator and faster than existing methods.
FreDN separates trends and periodicities in non-stationary time series forecasts.
problem Spectral entanglement and computational burden in frequency-domain methods for non-stationary time series.
method FreDN introduces a learnable Frequency Disentangler module to separate trend and periodic components directly in the frequency domain, and uses a ReIm Block to reduce complexity.
result FreDN outperforms state-of-the-art methods by up to 10% on long-term forecasting benchmarks.
Quantile-Frequency Analysis detects nonlinear dynamics in financial time series.
problem Detecting nonlinear dynamics in financial time series models.
method Quantile periodogram and trigonometric quantile regression.
result QFA provides additional insights into financial time series models.
WF distance measures time series similarity via spectral density displacement.
problem Measuring similarity between time series.
method Wasserstein-Fourier distance between normalised power spectral densities.
result WF establishes as a general-purpose metric for time series.
Study cryptocurrency price dynamics using adaptive EMD and spectral analysis.
problem Analyze the time-varying volatility of cryptocurrency prices.
method Adaptive complementary ensemble empirical mode decomposition (ACE-EMD) and Hilbert spectral analysis.
result Reveal the properties of various timescales in cryptocurrency price dynamics.
Framework clusters noisy MTS with robust fuzzy clustering, improving accuracy over existing methods.
problem Challenges in clustering multivariate time series due to non-stationary dependencies, noise, and state boundaries.
method Spectral fuzzy clustering using Kendall's tau-based canonical coherence for frequency-specific monotonic relationships.
result Framework outperforms existing methods in clustering noisy, high-dimensional MTS.
Develops a method to estimate network difference in high-dimensional time series data.
problem Estimating network differences in high-dimensional data can be unreliable.
method Uses an L1 penalty on the difference of inverse spectral densities to estimate network differences.
result Establishes consistency of the method for sparse network differences.
To a closed Riemannian manifold, we associate a set of (special values of) a family of Dirichlet series, indexed by functions on the manifold. We study the meaning of equality of two such families of spectral Dirichlet series under pullback along a map. This allows us to give a spectral characterization of when a smoot…
New method uses spectral series for fast, reliable inferences on complex data.
problem Making fast and reliable inferences for complex, high-dimensional data.
method Orthogonal series estimator based on kernel machine learning and Fourier methods.
result The spectral series approach adapts to the intrinsic geometry and dimension of the data.
High-dimensional inference for sparse spectral precision matrices
problem Inference on the spectral precision matrix at a fixed frequency
method Full likelihood-based inference using neighboring discrete Fourier transforms
result Simultaneous control of regularization, finite-sample truncation, and smoothing biases
HyFAD improves time series imputation by combining time and frequency diffusion.
problem Improve time series imputation by handling frequency-sensitive denoising and balancing global and local dynamics.
method HyFAD is a hybrid time-frequency diffusion model with frequency-aware embedding, built on DDPM paradigm.
result HyFAD achieves state-of-the-art performance in time series imputation.
A Python package solves source duplication in single channel LVMs using spectral regularisation.
problem Source duplication in LVMs hampers their practical use in single channel applications.
method Spectral regularisation term added to address source duplication issue.
result Spectral regularisation framework enables easier investigation and utilisation of LVMs.
Interactive privacy mechanisms improve spectral density estimation under local differential privacy.
problem Estimating spectral density of Gaussian time series with local differential privacy constraints.
method Two-stage process: Laplace mechanism followed by privatized sample analysis.
result Interactive mechanisms achieve faster rates for spectral density estimation.
Spectral method speeds fitting of binary time series models.
problem Modeling binary time series data with latent linear dynamical systems.
method Spectral learning of probit-Bernoulli latent linear dynamical systems.
result Spectral method provides robust, fixed-cost estimator.
Optimizes spectral density estimation for stationary and nonstationary processes.
problem Estimating spectral density of time series with complex structure.
method Optimally adaptive Bayesian spectral density estimation using smoothing spline covariance structure.
result Optimal eigendecomposition provides superior performance compared to alternative covariance functions.
Spectral methods predict long-term signals from linear and nonlinear systems.
problem Forecasting temporal signals from linear and nonlinear systems with arbitrary sampling.
method Introduces a spectral algorithm for linear signals and extends it to nonlinear systems using Koopman theory.
result The spectral methods achieve high accuracy in forecasting and uncertainty quantification.
Combines Fourier methods and RNNs for efficient time series prediction.
problem Efficiently processing and predicting time series data with memory and computational constraints.
method Uses short-time Fourier transform and weight reductions through low pass filtering in a Spectral RNN.
result Predicts time series data from chaotic systems and real-world data.
New method embeds correlation networks to reveal underlying time series patterns.
problem Analyzing correlation networks derived from time series data.
method Spectral embedding of noisy correlation networks, leveraging Fourier basis elements.
result Spectral embedding recovers true vertex-level latent representations under suitable assumptions.
Paper combines geometry and time-series analysis for spatiotemporal data.
problem Multivariate time-series data from multiple sensors.
method Combines manifold learning, Riemannian geometry, and spectral analysis.
result Proposes Riemannian multi-resolution analysis (RMRA) for dynamic mode extraction.
A new diffusion model improves time-series forecasting by preserving seasonal patterns.
problem Improving time-series forecasting accuracy, especially for seasonal data.
method A forward diffusion process that decomposes signals into spectral components, altering only the diffusion process.
result The method maintains high signal-to-noise ratios for dominant frequencies, improving long-term pattern recovery.
Microsoft develops a time-series anomaly detection service.
problem Real-time monitoring of various metrics in applications and services.
method Pipeline consisting of data ingestion, experimentation platform, and online compute; novel algorithm combining Spectral Residual and Convolutional Neural Network.
result Superior experimental results compared to state-of-the-art baselines on public and Microsoft production data.
Proposes a model for classifying high-dimensional time series with interpretable parameters.
problem Challenges in classifying high-dimensional time series, especially in neuroscience.
method Model-based approach using sparsity in inverse spectral density matrices, with interpretability of model parameters.
result Model demonstrates consistency and sure screening property, enabling nuanced inferences.
GACAN combines multi-granularity time series for traffic forecasting.
problem High dynamics and complex spatial-temporal dependency of road networks in traffic forecasting.
method Graph Attention-Convolution-Attention Networks (GACAN) with Att-Conv-Att (ACA) block.
result GACAN outperforms state-of-the-art baselines in traffic forecasting.
Robust clustering methods for multivariate time series data.
problem Clustering multivariate time series data robustly to outliers.
method Quantile-based fuzzy C-means with metric, noise, and trimmed approaches.
result Robust methods outperform alternatives in handling outlying series.
Researchers study spectral asymmetry using pseudodifferential projections on the massless Dirac operator.
problem Understanding spectral asymmetry for the massless Dirac operator.
method Constructing a negative order pseudodifferential asymmetry operator from spectral projections.
result Computed the principal symbol of the asymmetry operator, accounting for gauge invariance.
Study uses satellite data to predict tailings dam collapse risk.
problem Detecting early signs of tailings dam instability.
method Spectral analysis of satellite InSAR displacement time series data.
result Algorithm detects risk milestones up to 5 months before dam collapse.
A novel fuzzy clustering method for multivariate time series.
problem Clustering multivariate time series with varying dependencies and dynamics.
method Quantile-based cross-spectral features, PCA, fuzzy C-means, fuzzy C-medoids.
result Substantially outperforms existing methods in various evaluation schemes.
Study of spectral invariants on CR contact manifolds with circle action.
problem Analytic torsion and eta-like invariants on CR contact manifolds.
method Interpret spectral series topologically and dynamically using Reeb flow.
result Spectral series can be interpreted both topologically and dynamically.
New framework uses time series features for predicting streamflow in ungauged areas.
problem Predicting streamflow in areas without gauging stations.
method Developed regression-based streamflow regionalization using a wide range of time series features from large datasets.
result Certain time series features, like entropy and autocorrelation, are better predictors of streamflow than traditional catchment attributes.
Method detects lead-lag relationships in multivariate time series.
problem Discovering lead-lag relationships in multivariate time series.
method Clustering-driven methodology using sliding window and various clustering techniques.
result Robust lead-lag estimates across clusters enhance consistent relationships identification.
NFM models time-series data directly in the Fourier domain, achieving state-of-the-art performance.
problem Traditional time-series analysis focuses on the time domain, limiting flexibility.
method NFM models time-series data in the Fourier domain, using frequency extrapolation and interpolation.
result NFM achieves state-of-the-art performance on various time-series tasks.
Empirical analysis of the foreign exchange market is conducted based on methods to quantify similarities among multi-dimensional time series with spectral distances introduced in [A.-H. Sato, Physica A, 382 (2007) 258--270]. As a result it is found that the similarities among currency pairs fluctuate with the rotation …
This paper is the the third part of a series of paper whose aim is to use of the framework of \emph{twisted spectral triples} to study conformal geometry from a noncommutive geometric viewpoint. In this paper we reformulate the inequality of Vafa-Witten \cite{VW:CMP84} in the setting of twisted spectral triples. This i…
Earlier we proposed the stochastic point process model, which reproduces a variety of self-affine time series exhibiting power spectral density S(f) scaling as power of the frequency f and derived a stochastic differential equation with the same long range memory properties. Here we present a stochastic differential eq…
New kernels model non-stationary data efficiently.
problem Efficiently modeling non-stationary data with Gaussian processes.
method Model spectral density as a mixture of frequency surfaces, solve generalised Fourier transform.
result Derives efficient inference methods for non-stationary kernels.
Algorithm identifies fractal system's scaling exponents in high dimensions.
problem Statistical identification of Hurst distribution in high-dimensional fractal systems.
method Wavelet random matrices, modified spectral clustering, model selection.
result Algorithm consistently estimates Hurst distribution in moderately high dimensions.
Bayesian model improves spectral estimation from partial, noisy data.
problem Challenges in spectral estimation with partial and noisy observations.
method Joint probabilistic model with Gaussian process prior and Bayes' rule for exact inference.
result Proposed model provides functional-form representation of power spectral density.