Fermat-Torricelli points help assess investment risks by smoothing series data.
problem Analyzing investment risks in series with large variance, nonlinear trends, or non-normal distributions.
method Construct Fermat-Torricelli points to reduce random component influence.
result Smoothing series by Fermat-Torricelli points reduces risk assessment errors.
Efficient method classifies locally stationary time series based on second-order characteristics.
problem Classifying locally stationary time series for various applications.
method Autoregressive approximation, ensemble aggregation, distance-based threshold.
result Zero misclassification error rate asymptotically for mildly differing second-order characteristics.
The paper associates knots to numerical semigroups and shows their Alexander polynomials coincide with semigroups' Poincaré series.
problem Understanding the algebraic structure of numerical semigroups through topological representations.
method Associaing iterated torus knots to free numerical semigroups and analyzing their knot complements and Alexander polynomials.
result Alexander polynomials of knots associated with free numerical semigroups coincide with the semigroup's Poincaré series.
In this paper we derive a series expansion for the price of a continuously sampled arithmetic Asian option in the Black-Scholes setting. The expansion is based on polynomials that are orthogonal with respect to the log-normal distribution. All terms in the series are fully explicit and no numerical integration nor any …
In this report, we derive a non-negative series expansion for the Jensen-Shannon divergence (JSD) between two probability distributions. This series expansion is shown to be useful for numerical calculations of the JSD, when the probability distributions are nearly equal, and for which, consequently, small numerical er…
We derive analytic series representations for European option prices in polynomial stochastic volatility models. This includes the Jacobi, Heston, Stein-Stein, and Hull-White models, for which we provide numerical case studies. We find that our polynomial option price series expansion performs as efficiently and accura…
Derives a series expansion for Asian option pricing with polynomial jump-diffusion moments.
problem Pricing Asian options with polynomial jump-diffusion processes.
method Uses Hermite polynomials and moments of the underlying process for closed-form computation.
result Explicit computation of Greeks and accurate series expansion for Asian options.
This paper rates robustness of multi-modal time-series forecasting models.
problem Robustness of AI systems in time-series forecasting is crucial for stakeholders.
method Causal analysis to assess robustness of MM-TSFM models.
result Multi-modal forecasting models are more robust than numeric models.
Two algorithms improve fitting autoregressive models for big data.
problem Efficiently solving Toeplitz least squares problems for large time series data.
method Applied randomized numerical linear algebra (RandNLA) techniques.
result LSAR algorithm is more robust for real-world time series data.
Deep learning improves time series classification accuracy.
problem Classifying time series data efficiently.
method Developed deep neural networks for time series classification.
result Demonstrated superior performance of deep learning methods.
Multimodal analysis that uses numerical time series and textual corpora as input data sources is becoming a promising approach, especially in the financial industry. However, the main focus of such analysis has been on achieving high prediction accuracy while little effort has been spent on the important task of unders…
We derive a stronger uniqueness result if a function with compact support and its truncated Hilbert transform are known on the same interval by using the Sokhotski-Plemelj formulas. To find a function from its truncated Hilbert transform, we express them in the Chebyshev polynomial series and then suggest two methods t…
Non-parametric time series forecasting without assuming a specific distribution.
problem Time series forecasting with numerical stability issues in classical models.
method Generates predictions by sampling from the empirical distribution of time series data.
result The proposed method produces reasonable forecasts without numerical stability issues.
Proposes a new model for non-linear regression of multivariate time series data.
problem Regression models for non-scalar variables, especially time series, have limitations.
method Develops a non-linear function-on-function model using neural networks.
result Demonstrates effectiveness through real-world applications.
ST-GAN predicts stock trends using financial news and data.
problem Predicting financial trends in stock markets.
method ST-GAN combines NLP and technical indicators using GAN technology.
result Significant improvement over existing models in stock price forecasting.
Analyzes Kodaira-Iitaka dimension and multiplicity using intersection theory.
problem Understanding Kodaira-Iitaka dimension and multiplicity in analytic terms.
method Expresses dimensions and multiplicity in terms of intersection theory of plurisubharmonic envelopes.
result Introduces non-pluripolar numerical Kodaira-Iitaka dimension and shows it dominates the classical dimension.
Since the introduction and the public availability of the \textsc{ucr} time series benchmark data sets, numerous Time Series Classification (TSC) methods has been designed, evaluated and compared to each others. We suggest a critical view of TSC performance evaluation protocols put in place in recent TSC literature. Th…
The COS method proposed in Fang and Oosterlee (2008), although highly efficient, may lack robustness for a number of cases. In this paper, we present a Stable pricing of call options based on Fourier cosine series expansion. The Stability of the pricing methods is demonstrated by error analysis, as well as by a series …
ForecastGAN improves multi-horizon time series forecasting by integrating numerical and categorical features.
problem Limited performance of existing approaches in short-term and long-term forecasting.
method Decomposition, model selection, adversarial training.
result ForecastGAN consistently outperforms state-of-the-art transformer models for short-term forecasting.
Symbolic LSTM improves time series forecasting by reducing hyperparameter sensitivity.
problem High sensitivity to hyperparameters and random initialization in numerical time series forecasting.
method Combining LSTM with a dimension-reducing symbolic representation.
result Symbolic representation alleviates forecasting problems and speeds up training.
Artificial neural networks (ANNs) have very successfully been used in numerical simulations for a series of computational problems ranging from image classification/image recognition, speech recognition, time series analysis, game intelligence, and computational advertising to numerical approximations of partial differ…
Survey of deep learning methods for time series forecasting.
problem Improving accuracy in time series predictions across various domains.
method Analysis of common encoder and decoder designs, hybrid models, and decision support.
result Advancements in deep learning for time series forecasting.
Formula connects knot complements' invariants.
problem Understanding invariants of knot complements.
method Proposed a connect sum formula for two-variable series invariants.
result Numerical evidence supports the formula for various torus knots.
This paper compares two methods for training neural ODEs in time-series regression and CNFs.
problem Training neural ODEs for time-series regression and CNFs efficiently.
method Discretize-Optimize (Disc-Opt) vs. Optimize-Discretize (Opt-Disc) approaches.
result Disc-Opt methods can achieve similar performance as Opt-Disc at inference with drastically reduced training costs.
A new framework for generating predictive features in noisy multivariate time series.
problem Predicting noisy multivariate time series with limited user effort.
method Develops a feature programming framework based on spin-gas dynamical Ising models.
result Validated the method on synthetic and real-world datasets.
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. Paper analyzes Nyström regularization for time series forecasting with sequential sub-sampling.
problem Learning rate analysis of Nyström regularization for τ-mixing time series. method Banach-valued Bernstein inequality and integral operator approach for τ-mixing sequences. result Almost optimal learning rates for Nyström regularization with sequential sub-sampling.
Using classical Taylor series techniques, we develop a unified approach to pricing and implied volatility for European-style options in a general local-stochastic volatility setting. Our price approximations require only a normal CDF and our implied volatility approximations are fully explicit (ie, they require no spec…
TADA detects anomalies in time series using topological data analysis.
problem Detecting global changes in dependency structure between channels in multivariate time series.
method Topological Data Analysis for detecting anomalies in multivariate time series.
result The approach is more suitable for detecting global changes of correlation structures than existing methods.
We establish several closed pricing formula for various path-independent payoffs, under an exponential Lévy model driven by the Variance Gamma process. These formulas take the form of quickly convergent series and are obtained via tools from Mellin transform theory as well as from multidimensional complex analysis. Par…
Paper proposes a hybrid model for financial time series prediction using sentiment analysis.
problem Challenges in forecasting in non-stationary, complex environments with heterogeneous data.
method Hybrid model combining GANs with NLP-based sentiment analysis.
result Hybrid model enhances robustness in non-stationary environments.
Quantum model generates financial data with fewer parameters.
problem Generating financial data with fewer parameters.
method Applied time-series quantum generative model to financial data.
result Fewer parameters required compared to classical methods.
Motivated by numerical integration on manifolds, we relate the algebraic properties of invariant connections to their geometric properties. Using this perspective, we generalize some classical results of Cartan and Nomizu to invariant connections on algebroids. This has fundamental consequences for the theory of numeri…
New method for estimating high-dimensional binary time series coefficients.
problem Statistical inference for high-dimensional binary time series.
method Post-selection estimator and second-order wild bootstrap algorithm.
result Good finite-sample performance of the proposed method.
Proposes ridge regression on Riemannian manifolds for time-series prediction.
problem Time-series prediction on Riemannian manifolds.
method Combines Riemannian least-squares fitting via Bézier curves, empirical covariance on manifolds, and Mahalanobis distance regularization.
result Significant error reduction in synthetic spherical experiments and hurricane forecasting.
We establish an explicit pricing formula for the class of Lévy-stable models with maximal negative asymmetry (Log-Lévy model with finite moments and stability parameter 1<α≤2) in the form of rapidly converging series. The series is obtained with help of Mellin transform and the residue theory in C2. T…
A new SVM method for predicting time series labels.
problem Learning to predict labels from high-dimensional time series data.
method Extended SVM concept to continuous time series data, formulated as a convex optimization problem.
result Empirical results show the algorithm's effectiveness for analyzing long-term multivariate data.
Graph Neural Networks improve financial time series forecasting accuracy.
problem Forecasting univariate financial time series with statistical significance.
method Introducing the Time-Geometric model combining geometric and temporal patterns.
result Statistically significant improvements in forecasting accuracy through geometric patterns.
Paper introduces machine learning for time series data, improving nowcasting accuracy.
problem Improving accuracy in nowcasting US GDP growth using machine learning.
method Sparse-group LASSO estimator for high-dimensional time series data, considering different sampling frequencies and financial/macroeconomic data tail properties.
result Sparse-group LASSO outperforms unstructured LASSO in nowcasting US GDP growth.
We offer new formulas for European option pricing under tempered stable processes.
problem Pricing European options under tempered stable processes.
method Series expansions for tempered stable densities and European option prices.
result Our formulas are hyperparameter-free and competitive with traditional methods.
While ubiquitous, textual sources of information such as company reports, social media posts, etc. are hardly included in prediction algorithms for time series, despite the relevant information they may contain. In this work, openly accessible daily weather reports from France and the United-Kingdom are leveraged to pr…
CLWF improves time series imputation speed and accuracy.
problem Slow convergence in diffusion model-based imputation methods.
method CLWF uses Lagrangian mechanics to learn velocity and integrates a denoising autoencoder to estimate gradient.
result CLWF outperforms state-of-the-art imputation approaches.
Decomposing complex time series into trend, seasonality, and remainder components is an important task to facilitate time series anomaly detection and forecasting. Although numerous methods have been proposed, there are still many time series characteristics exhibiting in real-world data which are not addressed properl…
ALT improves TSC by capturing complex patterns in time series data.
problem Challenges in traditional TSC methods with time series complexity and variability.
method ALT incorporates variable-length shifted time windows to enhance LLT for better feature representation.
result ALT achieves state-of-the-art performance with few hyperparameters.
This note outlines a method for clustering time series based on a statistical model in which volatility shifts at unobserved change-points. The model accommodates some classical stylized features of returns and its relation to GARCH is discussed. Clustering is performed using a probability metric evaluated between post…
New resurgent analysis reveals dual q-series for Chern-Simons theory crossing natural boundaries.
problem Understanding crossing natural boundaries in Chern-Simons theory.
method Resurgent analysis and Mordell integrals to identify dual q-series. result Practical numerical algorithm generates dual q-series. In many scenarios, humans prefer a text-based representation of quantitative data over numerical, tabular, or graphical representations. The attractiveness of textual summaries for complex data has inspired research on data-to-text systems. While there are several data-to-text tools for time series, few of them try to …
Paper proposes a new efficient transport-based dissimilarity measure for time series classification.
problem Classifying time series with warping distortions.
method Defining a problem statement, proposing an Optimal Transport-based dissimilarity measure.
result The proposed method can solve the time series classification problem with reduced computational cost.