Paper develops online learning algorithms for quaternion ARMA models.
problem Adaptive learning for autoregressive moving average (ARMA) models in quaternion domain.
method Transformed learning problem into full information optimization task, solved using gradient descent and Newton's method.
result Online algorithms achieve asymptotic performance approaching best ARMA model.
ARMA nets expand receptive fields for dense prediction tasks.
problem Global information in dense prediction problems is challenging for traditional convolutional layers.
method ARMA layers with adjustable autoregressive coefficients replace traditional convolutions.
result ARMA networks improve dense prediction tasks including video prediction and semantic segmentation.
Study improves financial risk assessment using ARMA-APARCH-EVT models with HACs.
problem Improving risk assessment in financial portfolios.
method ARMA-APARCH-EVT-HAC model for volatility and extreme value forecasting.
result Empirical analysis shows the model's effectiveness in international stock market data.
New methods for estimating ARMA and GARCH models with stable noise.
problem Estimating parameters of ARMA and GARCH models with stable noise.
method Modified Hannan-Rissanen Method and Modified Empirical Characteristic Function for estimation.
result Efficiency, accuracy, and simplicity of proposed methods demonstrated through simulation.
Popular graph neural networks implement convolution operations on graphs based on polynomial spectral filters. In this paper, we propose a novel graph convolutional layer inspired by the auto-regressive moving average (ARMA) filter that, compared to polynomial ones, provides a more flexible frequency response, is more …
Algorithm learns graph ARMA processes for missing signal estimation.
problem Missing signal estimation in time-varying graph signals.
method Learning joint time-vertex power spectral density through convex relaxations.
result High accuracy in time-vertex signal estimation.
Improved ARMA-GARCH model for illiquid assets like cryptocurrencies.
problem Inadequate modeling of illiquid assets, especially cryptocurrencies, with traditional ARMA-GARCH models.
method Introducing liquidity-adjusted liquidity jump and diffusion metrics into ARMA-GARCH framework.
result The liquidity-adjusted model improves model fit and volatility sensitivity for cryptocurrencies.
ARMA cell simplifies neural autoregressive modeling for time series.
problem Complex RNN cells are not always necessary and can be inferior.
method Introduces ARMA cell, a simpler, modular approach for neural time series modeling.
result The ARMA cell is competitive with popular alternatives in performance.
GMMNs model cross-sectional dependence for better option pricing and simulation.
problem Modeling cross-sectional dependence between stochastic processes.
method Generative moment matching networks (GMMNs) for geometric Brownian motions and ARMA-GARCH models.
result GMMNs produce dependent quasi-random samples with variance reduction.
SALSA efficiently approximates leverage scores for big data, improving ARMA model fitting.
problem Efficiently approximating leverage scores for large matrices.
method Sequential approximate leverage-score algorithm (SALSA) using randomized numerical linear algebra.
result SALSA approximates leverage scores within (1+O(ε)) with high probability. One of the cornerstones of the field of signal processing on graphs are graph filters, direct analogues of classical filters, but intended for signals defined on graphs. This work brings forth new insights on the distributed graph filtering problem. We design a family of autoregressive moving average (ARMA) recursions,…
K-ARMA models cluster time series data robustly.
problem Clustering time series data effectively.
method Model-based K-ARMA clustering algorithm with robust outlier detection.
result K-ARMA models outperform existing methods for time series clustering.
We propose a mathematical procedure for finding informed traders in ultra-high frequency trading. We wrote it as Vector ARMA and found condition of its stationarity. For the price exposure complied with ARMA(1,2) we proved that underlying asset price difference can be derived as ARMA(1,1) process. For validation of the…
WAVE improves time series forecasting by integrating AR and MA components.
problem Time series forecasting challenges.
method WAVE attention mechanism with AR and MA components.
result WAVE attention consistently improves TSF performance.
Optimizes prediction error method for time-varying models.
problem Achieving optimal prediction error rates for time-varying models.
method Nonlinear least squares method for time-varying parametric models.
result First rate-optimal non-asymptotic analysis for time-varying models.
We propose a mathematical procedure for finding informed trader activities in European-style options and their underlying asset. The regression model (9) with moving average component was written. Being added to it ARMA-process for log-price differences of underlying asset, the generalized model is written as Vector AR…
This paper clusters networks with annotated time-series data using kernel-ARMA and Grassmannian geometry.
problem Clustering networks with annotated time-series data, including state, node, and subnetwork clustering.
method Extract features from time-series data using kernel-ARMA, map onto Grassmannian, and cluster using Riemannian geometry.
result The proposed framework outperforms state-of-the-art clustering schemes on brain-network data.
The study introduces new liquidity measures and models for assets with extreme liquidity.
problem Modeling assets with extreme liquidity, especially in crypto markets.
method Developed innovative liquidity premium measures, liquidity-adjusted return and volatility models, and used ARMA-GARCH/EGARCH models.
result The liquidity-adjusted models outperform traditional models in predicting asset performance at extreme liquidity.
Recursive filtering predicts wireless interference levels accurately.
problem Predicting interference in wireless networks.
method Designing a recursive predictor using Kalman filtering and ARMA model.
result Good accuracy of predicted interference values compared to true values.
A new method models volatile financial time series using v-transforms and copulas.
problem Modeling volatile financial time series with standard methods.
method v-transforms and copulas to describe and estimate time series with arbitrary marginal distributions and copula dynamics.
result The model replicates stylized facts of financial return series and facilitates risk quantification.
Bayesian ARMA model with directional shifts captures structural breaks in compositional time series.
problem Structural breaks in compositional time series due to external shocks or policy changes.
method Developed a Bayesian Dirichlet ARMA model augmented with a directional-shift intervention mechanism.
result The model captures structural breaks through interpretable parameters and produces coherent probabilistic forecasts.
Mid-LSTM improves midterm stock prediction accuracy.
problem Large cumulative errors in short-term deep learning models for midterm stock predictions.
method Mid-LSTM incorporates market trend as hidden states, using ARMA and LSTM.
result Mid-LSTM achieves 2-4% improvement in prediction accuracy on S&P 500 stocks.
Proposes a method for forecasting time series with multiple seasonality.
problem Forecasting time series with both short-term and long-term seasonality is challenging.
method Two-stage method: first generalizes ARMA model for multiple seasonality, second selects lag order.
result Method outperforms `Facebook Prophet` model in predictive performance.
Time series models generalize ARMA and ARFIMA with non-Gaussian dependence.
problem Modeling non-Gaussian serial dependence in time series data.
method Infinite-order partial copula dependence in s-vine processes.
result Rich class of models that generalize linear processes.
Study on quaternionic bisectional curvature for quaternion-Kähler manifolds.
problem Characterize quaternionic bisectional curvature on quaternion-Kähler manifolds.
method Analyzing properties of quaternionic bisectional curvature on specific manifolds.
result Non-negative quaternionic bisectional curvature is only on quaternionic projective space.
In this paper, we give the definitions and characterizations of quaternionic Salkowski, quaternionic anti-Salkowski and quaternionic similar curves in the Euclidean spaces E^3 and E^4. We obtain relationships between these curves and some special quaternionic curves such as quaternionic slant helices and quaternionic B…
We construct explicit left invariant quaternionic contact structures on Lie groups with zero and non-zero torsion, and with non-vanishing quaternionic contact conformal curvature tensor, thus showing the existence of quaternionic contact manifolds not locally quaternionic contact conformal to the quaternionic sphere. W…
The study finds conditions for quaternionic structures on symmetric spaces.
problem Conditions for quaternionic structures on symmetric spaces.
method Analysis of Lie group actions and representations.
result Symmetric spaces have invariant quaternionic structures under specific conditions.
We call a quaternionic Kaehler manifold with non-zero scalar curvature, whose quaternionic structure is trivialized by a hypercomplex structure, a hyper-Hermitian quaternionic Kaehler manifold. We prove that every locally symmetric hyper-Hermitian quaternionic Kaehler manifold is locally isometric to the quaternionic p…
We introduce a natural notion of quaternionic map between almost quaternionic manifolds and we prove the following, for maps of rank at least one: 1) A map between quaternionic manifolds endowed with the integrable almost twistorial structures is twistorial if and only if it is quaternionic. 2) A map between quaternion…
Defines quaternionic k-vector fields on quaternionic Kähler manifolds.
problem No specific problem stated; focuses on definition and properties.
method Introduced a modified Dirac operator to define quaternionic k-vector fields.
result Calculated the dimension of quaternionic k-vector fields on HPn. The paper uses Bayesian methods to infer hidden processes with unknown parameters.
problem Estimating hidden processes from noisy observations with unknown parameters.
method Variational Bayesian inference with autoregressive moving average (ARMA) and vector autoregressive (VAR) models, combined with sequential Monte Carlo (SMC) and importance sampling resampling (SISR).
result The proposed inference method accurately estimates hidden states from non-linear noisy observations.
The paper proves quaternion projective space is unstable.
problem Stability of quaternion projective space.
method Analyzing index of identity map on quaternion space forms.
result Quaternion projective space is unstable.
The paper studies quaternionic structures on GKM graphs and their relation to torus actions on quaternionic projective spaces.
problem Understanding quaternionic structures on GKM graphs and their implications for torus actions.
method Introducing quaternionic structures on GKM graphs and analyzing their properties in the context of torus actions.
result Abstract GKM graphs with specific 2-face structures correspond to torus actions on quaternionic projective spaces or Grassmannians.
Penrose's two-spinor notation for 4-dimensional Lorentzian manifolds can be extended to two-component notation for quaternionic manifolds, which is a very useful tool for calculation. We construct a family of quaternionic complexes over unimodular quaternionic manifolds by elementary calculation. On complex quaternio…
We introduce the notion of CR quaternionic map and we prove that any such real-analytic map, between CR quaternionic manifolds, is the restriction of a quaternionic map between quaternionic manifolds. As an application, we prove, for example, that for any submanifold M, of dimension 4k−1, of a quaternionic manifold…
The paper extends Gray's result to quaternion-Kähler manifolds.
problem Understanding quaternion-Kähler manifolds with non-negative quaternionic sectional curvature.
method Introducing quaternionic sectional curvature, proving Wolf spaces have non-negative curvature, and using nearly Kähler twistor spaces.
result Every quaternion-Kähler manifold with non-negative quaternionic sectional curvature is a Wolf space.
Quaternionic curves with specific torsion properties don't exist.
problem Existence of quaternionic Bertrand curves with non-zero torsion and bitorsion.
method Definition of quaternionic (1,3)-Bertrand curves using Type 2-Quaternionic Frame and Matsuda-Yorozu method.
result No quaternionic Bertrand curves with non-zero torsion and bitorsion exist.
A new QHR model extends HR model with a quadratic variance function.
problem Modeling volatility with greater flexibility and stationarity.
method Introducing a quadratic variance function to the HR model, maintaining Markovian property.
result Stationary distribution of the QHR model is Pearson type IV.
The conformal infinity of a quaternionic-Kahler metric on a 4n-manifold with boundary is a codimension 3-distribution on the boundary called quaternionic contact. In dimensions 4n-1 greater than 7, a quaternionic contact structure is always the conformal infinity of a quaternionic-Kahler metric. On the contrary, in dim…
Quaternionic differential geometry expands geometric concepts using quaternions.
problem Generalizing geometric concepts to quaternionic constraints.
method Generalizing curves and surfaces, curvature, torsion, differential forms, and directional derivatives to quaternionic constraints.
result Quaternionic formalism provides a suitable language for differential geometry.
Modelled on a real hypersurface in a quaternionic manifold, we introduce a quaternionic analogue of CR structure, called quaternionic CR structure. We define the strong pseudoconvexity of this structure as well as the notion of quaternionic pseudohermitian structure. Following the construction of the Tanaka-Webster con…
The paper classifies compact affine quaternionic curves and surfaces.
problem Classifying compact affine quaternionic curves and surfaces.
method Affine quaternionic manifolds, Kodaira Theorem, fundamental groups, Lie Groups.
result Only quaternionic tori and primary Hopf surface S^3 x S^1 are compact affine quaternionic curves.
The paper explores quaternionic curves using differential geometry.
problem Understanding quaternionic curves.
method Differential geometry applied to quaternionic curves.
result Simpler formulations of quaternionic curves.
Quaternionic Brownian motion on flag manifold linked to sphere diffusion.
problem Modeling quaternionic stochastic areas on quaternionic flag manifolds.
method Relating quaternionic Brownian motion to symplectic Brownian motion and using radial dynamics.
result Quaternionic stochastic areas follow a multivariate normal distribution.
Study cohomology of quaternionic foliations and orbifolds.
problem Understanding cohomology of quaternionic foliations and orbifolds.
method Definition and proof of foliated versions of classical results for quaternionic Kähler manifolds.
result Formulation and proof of foliated versions of classical results for quaternionic Kähler manifolds.
Motivated by the quaternionic geometry corresponding to the homogeneous complex manifolds endowed with (holomorphically) embedded spheres, we introduce and initiate the study of the `quaternionic-like manifolds'. These contain, as particular subclasses, the CR quaternionic and the ρ-quaternionic manifolds. Moreover, …
Study counts and equidistributes rational points in quaternionic Heisenberg groups.
problem Counting and equidistribution of rational points in quaternionic Heisenberg groups.
method Arithmetic group actions on quaternionic hyperbolic spaces, Mertens counting formula, Neville equidistribution theorem.
result Proved Mertens counting formula and Neville equidistribution theorem for rational points over definite quaternion algebras.