arXiv research

Researchers discover all affinely homogeneous models for surfaces in 4D space.

Robust CD method for real-world time series with power-law distributions.

We focus on power-law coherency as an alternative approach towards studying power-law cross-correlations between simultaneously recorded time series. To be able to study empirical data, we introduce three estimators of the power-law coherency parameter $H_ρ$ based on popular techniques usually utilized for studying pow…

This research evaluates measures of dependence for financial time-series data.

A robust model handles up to 25% of outliers in time-series data for power flow calculations.

We study finite sample properties of estimators of power-law cross-correlations -- detrended cross-correlation analysis (DCCA), height cross-correlation analysis (HXA) and detrending moving-average cross-correlation analysis (DMCA) -- with a special focus on short-term memory bias as well as power-law coherency. Presen…

New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.

Driven by climatic processes, wind power generation is inherently variable. Long-term simulated wind power time series are therefore an essential component for understanding the temporal availability of wind power and its integration into future renewable energy systems. In the recent past, mainly power curve based mod…

The loop invariants of Dimofte-Garoufalidis is a formal power series with arithmetically interesting coefficients that conjecturally appears in the asymptotics of the Kashaev invariant of a knot to all orders in $1/N$. We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power se…

A new test for volatility in clustered time series data, robust to distributional assumptions.

Our aim is to prove that two formal power series of importance to quantum topology are Gevrey. These series are the Kashaev invariant of a knot (reformulated by Huynh and the second author) and the Gromov norm of the LMO of an integral homology 3-sphere. It follows that the power series associated to a simple Lie algeb…

Wind power prediction is of vital importance in wind power utilization. There have been a lot of researches based on the time series of the wind power or speed, but In fact, these time series cannot express the temporal and spatial changes of wind, which fundamentally hinders the advance of wind power prediction. In th…

Analysis of long-range dependence in financial time series was one of the initial steps of econophysics into the domain of mainstream finance and financial economics in the 1990s. Since then, many different financial series have been analyzed using the methods standardly used outside of finance to deliver some importan…

By use of a natural map introduced recently by the first and third authors from the space of pure-type complex differential forms on a complex manifold to the corresponding one on the small differentiable deformation of this manifold, we will give a power series proof for Kodaira-Spencer's local stability theorem of Kä…

Adaptive Bayesian model for covariate-dependent power spectra analysis.

Style Miner generates stable and significant style factors for time series analysis.

We provide analytical tools for pricing power options with exotic features (capped or log payoffs, gap options ...) in the framework of exponential Lévy models driven by one-sided stable or tempered stable processes. Pricing formulas take the form of fast converging series of powers of the log-forward moneyness and of …

The paper is concerned with the Kontsevich-Zagier formal power series $f(q)=\sum_{n=0}^\infty (1-q)... (1-q^n)$ and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series $F(x)=e^{-1/(24x)}f(e^{-1/x})$ from which its analytic continuation, i…

Here we propose a method, based on detrended covariance which we call detrended cross-correlation analysis (DXA), to investigate power-law cross-correlations between different simultaneously-recorded time series in the presence of non-stationarity. We illustrate the method by selected examples from physics, physiology,…

Method identifies causal interactions between time series using extreme eigenvalue variability.

Power series invariant of hyperbolic 3-manifolds matches knot invariants.

One of the first steps to understand and forecast economic downturns is identifying their frequency distribution, but it remains uncertain. This problem is common in phenomena displaying power-law-like distributions. Power laws play a central role in complex systems theory; therefore, the current limitations in the ide…

The paper develops a method for forecasting power consumption at various levels of aggregation.

We prove Fu's power series conjecture which relates the algebra of isometry invariant valuations on complex space forms to a formal power series from combinatorics which was introduced by Tutte. The $n$-th coefficient of this series is the number of triangulations of a triangle with $3n$ internal edges; or the number o…

GeoStat simplifies time series classification with fast, intuitive features.

Paper detects and estimates breaks in high-dimensional functional time series.

Improved time series classification with imputed data using label-guided forest-based methods.

Optimal sampling reduces power grid data analysis costs.

We calculate the second coefficient of the asymptotic expansion of the Bergman kernel of the Hodge-Dolbeault operator associated to high powers of a Hermitian line bundle with non-degenerate curvature, using the method of formal power series developed by Ma and Marinescu.

We consider stochastic point processes generating time series exhibiting power laws of spectrum and distribution density (Phys. Rev. E 71, 051105 (2005)) and apply them for modeling the trading activity in the financial markets and for the frequencies of word occurrences in the language.

The Habiro ring of a number field uses power series to study algebraic K-theory.

In this paper, we propose a variable selection method for general nonparametric kernel-based estimation. The proposed method consists of two-stage estimation: (1) construct a consistent estimator of the target function, (2) approximate the estimator using a few variables by l1-type penalized estimation. We see that the…

The authors seek financial datasets to benchmark feature engineering methods on US market data.

We study the properties of memory of a financial time series adopting two different methods of analysis, the detrended fluctuation analysis (DFA) and the analysis of the power spectrum (PSA). The methods are applied on three time series: one of high-frequency returns, one of shuffled returns and one of absolute values …

PPBoot simplifies prediction-powered inference.

Paper benchmarks and customizes energy forecasting methods.

Spectral Independence Criterion helps infer cause-effect relationships in time series.

We analyze the European transition economies and show that time series for most of major indices exhibit (i) power-law correlations in their values, power-law correlations in their magnitudes, and (iii) asymmetric probability distribution. We propose a stochastic model that can generate time series with all the previou…

When common factors strongly influence two power-law cross-correlated time series recorded in complex natural or social systems, using classic detrended cross-correlation analysis (DCCA) without considering these common factors will bias the results. We use detrended partial cross-correlation analysis (DPXA) to uncover…

We discuss how maximum entropy methods may be applied to the reconstruction of Markov processes underlying empirical time series and compare this approach to usual frequency sampling. It is shown that, at least in low dimension, there exists a subset of the space of stochastic matrices for which the MaxEnt method is mo…

This paper extends hypergraph construction to multivariate time series using signature transforms.

A method for estimating the cross-correlation $C_{xy}(τ)$ of long-range correlated series $x(t)$ and $y(t)$, at varying lags $τ$ and scales $n$, is proposed. For fractional Brownian motions with Hurst exponents $H_1$ and $H_2$, the asymptotic expression of $C_{xy}(τ)$ depends only on the lag $τ$ (wide-sense stationarit…

The entropy density is an intuitive and powerful concept to study the complicated nonlinear processes derived from physical systems. We develop the minimum entropy density method (MEDM) to detect the structure scale of a given time series, which is defined as the scale in which the uncertainty is minimized, hence the p…

Investigations have been performed into using clustering methods in data mining time-series data from smart meters. The problem is to identify patterns and trends in energy usage profiles of commercial and industrial customers over 24-hour periods, and group similar profiles. We tested our method on energy usage data p…

Recently, the visibility graph has been introduced as a novel view for analyzing time series, which maps it to a complex network. In this paper, we introduce new algorithm of visibility, "cross-visibility", which reveals the conjugation of two coupled time series. The correspondence between the two time series is mappe…

DeepLINK-T uses deep learning and knockoffs for time series data.

In the context of stochastic volatility models, we study representation formulas in terms of expectations for the power series' coefficients associated to the call price-function. As in a recent paper by Antonelli and Scarlatti the expansion is done w.r.t. the correlation between the noises driving the underlying asset…

In every point of a Kähler manifold there exist special holomorphic coordinates well adapted to the underlying geometry. Comparing these Kähler normal coordinates with the Riemannian normal coordinates defined via the exponential map we prove that their difference is a universal power series in the curvature tensor and…