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…
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48 results for “power series”
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…
A robust model handles up to 25% of outliers in time-series data for power flow calculations.
problem Handling outliers in time-series data for accurate power flow calculations.
method Robust data-driven process model with Schweppe-type generalized maximum likelihood estimator and projection statistics for outlier weighting.
result The model can handle up to 25% of outliers in the training data set.
This research evaluates measures of dependence for financial time-series data.
problem Accurately preparing time series data and selecting an appropriate measure of dependence is challenging.
method Review and establishment of a comprehensive analysis framework for shaping time-series data and evaluating measures of dependence.
result A method, framework, and example for selecting and evaluating a suitable measure of dependence are presented.
The paper is concerned with the Kontsevich-Zagier formal power series and its analytic properties. To begin with, we give an explicit formula for the Borel transform of the associated formal power series from which its analytic continuation, i…
Robust CD method for real-world time series with power-law distributions.
problem Challenges in causal discovery due to noise sensitivity.
method Power-law spectral feature extraction for robust CD.
result Consistently outperforms state-of-the-art alternatives on real-world datasets.
Researchers discover all affinely homogeneous models for surfaces in 4D space.
problem Identifying all affinely homogeneous models for surfaces in 4D space.
method Improved power series method of equivalence, capturing invariants at the origin, creating branches, and infinitesimalizing calculations.
result Find several inequivalent terminal branches yielding each to some nonempty moduli space of homogeneous models.
Fractal approach towards power-law coherency to measure cross-correlations between time seriesq-fin.ST
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 based on popular techniques usually utilized for studying pow…
Power series invariant of hyperbolic 3-manifolds matches knot invariants.
problem Understanding topological invariants of hyperbolic 3-manifolds.
method Perturbative power series associated with ideally triangulated cusped hyperbolic 3-manifolds.
result The power series agrees with Kashaev and Andersen-Kashaev invariants to all orders.
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 -th coefficient of this series is the number of triangulations of a triangle with internal edges; or the number o…
New method detects intrinsic cross-correlations in non-stationary time series affected by common factors.
problem Bias in cross-correlation analysis due to common external factors.
method Multifractal temporally weighted detrended partial cross-correlation analysis (MF-TWDPCCA).
result MF-TWDPCCA accurately detects intrinsic cross-correlations between non-stationary time series.
Paper detects and estimates breaks in high-dimensional functional time series.
problem Detecting and estimating structural breaks in heterogeneous mean functions of high-dimensional functional time series.
method Proposes a new test statistic combining functional CUSUM and power enhancement components, with a clustering algorithm for group structure estimation.
result The proposed techniques have satisfactory performance in finite samples, detecting and estimating breaks effectively.
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.
problem Analyzing algebraic K-theory of number fields.
method Introduces Habiro ring and modules graded by .
result Establishes connections between Habiro ring and Chern-Simons theory.
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…
Violation of market efficiency in transition economiesphysics.soc-ph
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…
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…
A new test for volatility in clustered time series data, robust to distributional assumptions.
problem Volatility issues in clustered multiple time series data, especially in stock market indicators.
method Bootstrap method for multiple time series, accounting for contagion effect.
result The test is correctly sized and powerful, especially for stationary mean and contained volatility in fewer clusters.
Coupling between time series: a network viewphysics.data-an
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…
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…
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 . We develop methods implemented in SnapPy that compute the first 6 coefficients of the formal power se…
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…
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 develops a method for forecasting power consumption at various levels of aggregation.
problem Forecasting power consumption at different levels of household aggregation.
method Three-step process: feature generation, aggregation, and projection.
result The method provides theoretical guarantees on prediction error and performs well on real data.
Adaptive Bayesian model for covariate-dependent power spectra analysis.
problem Estimating complex relationships and interactions between covariates and power spectra.
method Bayesian sum of trees model with local power spectrum estimation and reversible-jump MCMC for tree modifications.
result The method can accurately recover both smooth and abrupt changes in power spectra across multiple covariates.
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…
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…
Style Miner generates stable and significant style factors for time series analysis.
problem Finding significant and stable explanatory factors in high-dimensional time series data.
method Proposes a reinforcement learning method to balance explanatory power and stability constraints.
result Outperforms existing methods by a large margin and achieves a 10% gain in R-squared explanatory power.
The increasing importance of renewable energy, especially solar and wind power, has led to new forces in the formation of electricity prices. Hence, this paper introduces an econometric model for the hourly time series of electricity prices of the European Power Exchange (EPEX) which incorporates specific features like…
Lueck expressed the Gromov norm of a knot complement in terms of an infinite series that can be computed from a presentation of the fundamental group of the knot complement. In this note we show that Lueck's formula, applied to torus knots, yields surprising power series expansions for the logarithm function. This gene…
Conditions for torsion-free connections with specific curvature maps are derived.
problem Finding conditions for torsion-free connections with prescribed curvature.
method Using a power series approach to derive necessary and sufficient conditions for a curvature map to arise from a torsion-free connection.
result A unique torsion-free connection is derived from a given curvature map.
New framework for tracking varying bounds in time series forecasting.
problem Forecasting bounded time series with varying bounds.
method Extended log-likelihood estimation, online maximum likelihood estimation, Normalized Gradient Descent (NGD) for quasiconvex optimization.
result Derive an Online Normalized Gradient Descent algorithm for online bound tracking.
Modelling share volume traded in financial marketscond-mat.stat-mech
A simple analytically solvable model exhibiting a 1/f spectrum in an arbitrarily wide frequency range was recently proposed by Kaulakys and Meskauskas (KM). Signals consisting of a sequence of pulses show that inherent origin of the 1/f noise is Brownian fluctuations of the average intervent time between subsequent pul…
Proves resurgence properties for Habiro elements from radial limits of theta series.
problem Proving resurgence properties for Habiro elements.
method Using strange identities and Borel transform of formal power series.
result Proves Costin and Garoufalidis conjecture for two families of torus knots.
Dimofte, Gaiotto and Gukov introduced a powerful invariant, the 3D-index, associated to a suitable ideal triangulation of a 3-manifold with torus boundary components. The 3D-index is a collection of formal power series in with integer coefficients. Our goal is to explain how the 3D-index is a generating serie…
We construct power series invariants of rational homology 3-spheres from quantum PSU(n)-invariants. The power series can be regarded as perturbative invariants corresponding to the contribution of the trivial connection in the hypothetical Witten's integral. This generalizes a result of Ohtsuki (the case) which l…
Order flow in the financial markets from the perspective of the Fractional Lévy stable motionq-fin.ST
The study examines order flow in financial markets using fractional Lévy stable motion.
problem Challenges in selecting the best models for financial time series data.
method Investigates order disbalance time series from the perspective of fractional Lévy stable motion.
result Orders exhibit stable anti-correlation for 18 randomly selected stocks.
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 Quantum Modularity Conjecture of Zagier predicts the existence of a formal power series with arithmetically interesting coefficients that appears in the asymptotics of the Kashaev invariant at each root of unity. Our goal is to construct a power series from a Neumann-Zagier datum (i.e., an ideal triangulation of th…
DeepLINK-T uses deep learning and knockoffs for time series data.
problem Interpreting and reproducible deep learning models for high-dimensional time series data.
method Combines deep learning with knockoffs for FDR control in feature selection for time series models.
result DeepLINK-T effectively controls FDR while demonstrating superior feature selection for high-dimensional longitudinal time series data.
We extend our previous study of scaling range properties done for detrended fluctuation analysis (DFA) \cite{former_paper} to other techniques of fluctuation analysis (FA). The new technique called Modified Detrended Moving Average Analysis (MDMA) is introduced and its scaling range properties are examined and compared…
Lie-Butcher (LB) series are formal power series expressed in terms of trees and forests. On the geometric side LB-series generalizes classical B-series from Euclidean spaces to Lie groups and homogeneous manifolds. On the algebraic side, B-series are based on pre-Lie algebras and the Butcher-Connes-Kreimer Hopf algebra…
Paper develops a weighted linearization approach for vector fields.
problem Linearizability of vector fields under weighted conditions.
method Formal Moser trick applied to power series, addressing weighted non-resonance condition.
result Formal Moser trick works over any field of characteristic zero.
Dynamic scaling approach to study time series fluctuationsphysics.data-an
We propose a new approach for properly analyzing stochastic time series by mapping the dynamics of time series fluctuations onto a suitable nonequilibrium surface-growth problem. In this framework, the fluctuation sampling time interval plays the role of time variable, whereas the physical time is treated as the analog…
Method identifies causal interactions between time series using extreme eigenvalue variability.
problem Detecting causal interactions between time series.
method Largest eigenvalue of lagged correlation matrices, measuring causal interactions through variability.
result The method outperforms traditional Granger causality tests in detecting structural changes.
Adaptive estimation for nonstationary time series reduces computational cost.
problem Estimating parameters of nonstationary time series with varying parameters over time.
method Moving exponential moving ML estimator for scale parameter estimation.
result Significantly improved log-likelihoods compared to standard estimation.
Study higher genus polylogarithms under Riemann surface degenerations.
problem Understanding higher genus polylogarithms under degenerations.
method Investigate the Enriquez connection for polylogarithms and show it becomes a known connection for families of Riemann surfaces.
result Higher genus polylogarithms can be described explicitly as power series in deformation parameters and logarithms of families.