We study the ergodic properties of compositions of interval exchange transformations and rotations. We show that for any interval exchange transformation T, there is a full measure set of αin [0, 1) so that T composed with R_α is uniquely ergodic, where R_α is rotation by α.
On-device research index
arXiv research
A locally-built, LLM-digested index of recent arXiv papers in quant finance, geometry/topology, and statistical ML — keyword search served straight from SQLite on this machine.
168,695 papers · 148 categories
Trend · papers per month
48 results for “interval exchange transformations”
In [Mas82] and [Vee78] it was proved independently that almost every interval exchange transformation is uniquely ergodic. The Birkhoff ergodic theorem implies that these maps mainly have uniformly distributed orbits. This raises the question under which conditions the orbits yield low-discrepancy sequences. The case o…
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch which we call non-classical interval exchanges, form a subclass of linear involutions without flips. They are analogs of classical interval exchanges, and are…
This paper presents quantitative shrinking target results for rotations and interval exchange transformations. To do this a quantitative version of a unique ergodicity criterion of Boshernitzan is established.
It is known since 40 years old paper by M. Keane that minimality is a generic (i.e. holding with probability one) property of an irreducible interval exchange transformation. If one puts some integral linear restrictions on the parameters of the interval exchange transformation, then minimality may become an "exotic" p…
Graphs from van der Corput sequence embed into Chamanara surface.
problem Embedding graphs from van der Corput sequence into surfaces.
method Constructed -regular graphs from van der Corput sequence and Kronecker sequence, embedded into torus and Chamanara surface.
result Graphs from van der Corput sequence embed into Chamanara surface with one edge removal.
Let be a non-degenerate permutation on at least symbols. We show that the set of uniquely ergodic interval exchange transformations with permutation is path-connected.
Study of SL(2,R) representations on a once-punctured torus, showing Cantor set spectrum.
problem Characterizing SL(2,R) representations on a once-punctured torus.
method Introduction of spectrum as a subset of projective measured laminations, analysis of dynamics of cocycles.
result Spectrum of a generic representation on a once-punctured torus is a Cantor set.
Multiple conventions have been adopted for denoting Interval Exchange Transformations (IETs). The "non-labeled" convention was the original, while the "labeled" convention has proven convenient when investigating Flat Surfaces as described by IETs. We establish the relationship between Extended Rauzy Classes, an equiva…
Interval exchange maps are related to geodesic flows on translation surfaces; they correspond to the first return maps of the vertical flow on a transverse segment. The Rauzy-Veech induction on the space of interval exchange maps provides a powerful tool to analyze the Teichmueller geodesic flow on the moduli space of …
A natural generalization of interval exchange maps are linear involutions, first introduced by Danthony and Nogueira. Recurrent train tracks with a single switch provide a subclass of linear involutions. We call such linear involutions non-classical interval exchanges. They are related to measured foliations on orienta…
Book explores infinite translation surfaces, challenging traditional geometry.
problem Understanding infinite-type translation surfaces.
method Detailed classification, construction, and analysis of symmetries.
result Complex dynamics in infinite-type translation flows.
We show that there exists an interval exchange and a point so that the orbit of the point equidistributes for a measure that is not ergodic.
Foam cobordism groups linked to interval exchange automorphisms.
problem Understanding cobordism groups of foams.
method Using the Sah-Arnoux-Fathi invariant and K-theory.
result Identified cobordism groups with homology and K-groups.
Skew-adaptive method improves prediction intervals for regression.
problem Improving prediction intervals for regression models, especially in cases of skewness and varying scales.
method Develops a skew-adaptive extension of split conformal prediction using an asymmetric interval family and gauge approach.
result Preserves marginal validity and adapts to local scale and skewness, with efficiency gains over existing methods.
Connected components of the moduli spaces of Abelian differentials with prescribed singularitiesmath.GT
Consider the moduli space of pairs (C,w) where C is a smooth compact complex curve of a given genus and w is a holomorphic 1-form on C with a given list of multiplicities of zeroes. We describe connected components of this space. This classification is important in the study of dynamics of interval exchange transformat…
We started from computer experiments with simple one-dimensional ergodic dynamical systems called interval exchange transformations. Correlators in these systems decay as a power of time. In the simplest non-trivial case the exponent is equal to 1/3. We found a formula connecting characteristic exponents with explicit …
Constructs tail-specific prediction intervals for financial applications
problem Financial applications require strict control on the left tail
method Extends classical conformal frameworks to provide explicit tail-specific guarantees
result Improved directional calibration in skewed data
Develops efficient time series prediction intervals.
problem Constructing reliable prediction intervals for time series data.
method Introduces exttt{EnbPI} algorithm for time series data.
result Demonstrates superior performance compared to existing methods.
An online framework optimizes efficiency in conformal prediction with a target miscoverage rate.
problem Achieving coverage and minimizing interval length in a sequential, online setting.
method Optimizes efficiency by directly optimizing the average length of intervals while maintaining coverage.
result Shows a gap between optimal performance for exchangeable and arbitrary sequences, and provides a matching algorithm for the Pareto-optimal settings.
Wavelet denoised-ResNet with LightGBM predicts Forex rate of change.
problem Forecasting Foreign Exchange (Forex) rate of change for trading opportunities.
method Wavelet denoising, ResNet, LightGBM, technical indicators, image features.
result The model outperforms baseline models with low MAE, MSE, and RMSE.
Novel method for time-series prediction with tighter confidence intervals.
problem Improving prediction intervals for time-series data.
method Kernel-based Optimally Weighted Conformal Prediction Intervals (KOWCPI) using adaptive weights.
result KOWCPI achieves narrower confidence intervals with guaranteed coverage.
LLT improves cryptocurrency price movement prediction accuracy.
problem Predicting intraday price movements of cryptocurrencies.
method Linear law-based feature space transformation (LLT) applied to cryptocurrency price data.
result LLT significantly enhances prediction accuracy for all cryptocurrencies.
Ehrenfest Model with Large Jumps in Financecond-mat.stat-mech
Changes (returns) in stock index prices and exchange rates for currencies are argued, based on empirical data, to obey a stable distribution with characteristic exponent for short sampling intervals and a Gaussian distribution for long sampling intervals. In order to explain this phenomenon, an Ehrenfest model…
The family of translation surfaces constructed by Arnoux and Yoccoz from self-similar interval exchange maps encompasses one example from each genus greater than or equal to . We triangulate these surfaces and deduce general properties they share. The surfaces converge to a surface $(X_\i…
Method constructs prediction intervals for time-varying individual treatment effects.
problem Accurately quantify uncertainty of individual treatment effects across multiple decision points.
method Conformal inference techniques for time-varying ITEs with weaker assumptions.
result Guaranteed lower bound for coverage dependent on data non-exchangeability.
We prove a computable version of de Finetti's theorem on exchangeable sequences of real random variables. As a consequence, exchangeable stochastic processes expressed in probabilistic functional programming languages can be automatically rewritten as procedures that do not modify non-local state. Along the way, we pro…
A new algorithm for time series prediction intervals.
problem Non-exchangeability in time series data.
method Adaptive re-estimation of non-conformity scores.
result Significant reduction in interval width compared to existing methods.
Power law for the calm-time interval of price changescond-mat.stat-mech
In this paper, we describe a newly discovered statistical property of time series data for daily price changes. We conducted quantitative investigation of the {\it calm-time intervals} of price changes for 800 companies listed in the Tokyo Stock Exchange, and for the Nikkei 225 index over a 27-year period from January …
A new method for pricing exchange options under stochastic volatility and jumps.
problem Pricing European and American exchange options with stochastic volatility and jumps.
method Equivalent martingale measure, numeraire choice, integral transforms, Kolmogorov backward equation, integral equations.
result Reduced exchange option pricing to a one-dimensional problem of a call option.
It is well known that in models with time-homogeneous local volatility functions and constant interest and dividend rates, the European Put prices are transformed into European Call prices by the simultaneous exchanges of the interest and dividend rates and of the strike and spot price of the underlying. This paper inv…
We prove that square-tiled surfaces having fixed combinatorics of horizontal cylinder decomposition and tiled with smaller and smaller squares become asymptotically equidistributed in any ambient linear -invariant suborbifold defined over in the moduli space of Abelian differentials. Moreover…
Fluctuations in time intervals of financial data from the view point of the Gini indexphysics.data-an
We propose an approach to explain fluctuations in time intervals of financial markets data from the view point of the Gini index. We show the explicit form of the Gini index for a Weibull distribution which is a good candidate to describe the first passage time of foreign exchange rate. The analytical expression of the…
New method makes CP intervals locally adaptive using trainable transformations.
problem Making Conformal Prediction intervals locally adaptive.
method Defining a trainable change of variables that depends on object attributes .
result Locally adaptive prediction intervals with guaranteed marginal validity and variable sizes.
Conformalized Super Learnerstat.ML
A new method combines conformal prediction with Super Learner for interval predictions.
problem Constructing reliable interval predictions for complex regression functions.
method Coupling conformal prediction with Super Learner framework.
result The conformalized SL achieves valid finite-sample coverage with competitive performance.
Flexible method for estimating frequencies in large datasets using sketching.
problem Estimating frequencies in very large datasets efficiently and accurately.
method Data-adaptive conformal inference method based on a smaller sketch of data.
result Proves validity of frequentist confidence intervals under data exchangeability.
Practical or scientific considerations often lead to selecting a subset of parameters as ``important.'' Inferences about those parameters often are based on the same data used to select them in the first place. That can make the reported uncertainties deceptively optimistic: confidence intervals that ignore selection g…
Nonstationary Increments, Scaling Distributions, and Variable Diffusion Processes in Financial Marketsphysics.soc-ph
Arguably the most important problem in quantitative finance is to understand the nature of stochastic processes that underlie market dynamics. One aspect of the solution to this problem involves determining characteristics of the distribution of fluctuations in returns. Empirical studies conducted over the last decade …
Flat Surfacesmath.DS
Various problems of geometry, topology and dynamical systems on surfaces as well as some questions concerning one-dimensional dynamical systems lead to the study of closed surfaces endowed with a flat metric with several cone-type singularities. Such flat surfaces are naturally organized into families which appear to b…
Modeling stock price dynamics on the Ghana Stock Exchange: A Geometric Brownian Motion approachmath.OC
Study finds GBM model accurately predicts stock prices on Ghana Stock Exchange.
problem Investigating the suitability of GBM for modeling stock price dynamics.
method Geometric Brownian Motion model applied to weekly and monthly returns of equities listed on the Ghana Stock Exchange.
result GBM model accurately forecasts stock prices with minimal deviations, as evidenced by MSE evaluations.
Boosting methods for interval-censored data improve predictive accuracy in survival analysis.
problem Handling interval-censored data in survival analysis and time-to-event studies.
method Nonparametric boosting methods using censoring unbiased transformations and functional gradient descent.
result Effective boosting methods for regression and classification with interval-censored data, offering robust performance.
The paper introduces a method to assess machine translation quality with confidence intervals.
problem Evaluating the uncertainty and quality of machine translation.
method Utilizes conformal predictive distributions to produce prediction intervals with guaranteed coverage.
result The method outperforms a baseline on six language pairs in terms of coverage and sharpness.
Two methods are proposed to filter correlations in DCC-GARCH residuals for foreign exchange rates.
problem Filtering correlations in DCC-GARCH residuals for accurate foreign exchange rate prediction.
method Two approaches: estimating correlation matrix as a parameter and using eigenvalue decomposition.
result The DCC-GARCH residual can be almost independent using these methods.
A new method for time-series data provides guaranteed coverage and adapts to non-exchangeable data.
problem Guaranteed coverage for time-series data prediction intervals.
method Sequential Conformalized Density Regions (SCDR) using quantile random forest.
result SCDR achieves guaranteed asymptotic coverage and outperforms existing methods in simulations.
Paper introduces detect-then-impute conformal prediction for cellwise outliers.
problem Uncertainty in prediction intervals for models with cellwise outliers.
method Detects outliers, imputes them, and constructs exchangeable features for conformal prediction.
result JDI-CP achieves a finite sample coverage guarantee.
Heisenberg Translation Flowsmath.DS
Study of flows on circle bundles over translation surfaces, showing decay of correlations.
problem Ergodic properties of flows on circle bundles over translation surfaces.
method Generalizing Heisenberg nilflows to more general base surfaces, showing relatively mixing.
result Showed that such flows exhibit decay of correlations in the orthogonal complement of functions constant along fibers.
We introduce a deterministic dealer model which implements most of the empirical laws, such as fat tails in the price change distributions, long term memory of volatility and non-Poissonian intervals. We also clarify the causality between microscopic dealers' dynamics and macroscopic market's empirical laws.
Power Laws and Gaussians for Stock Market Fluctuationsphysics.soc-ph
The daily volume of transaction on the New York Stock Exchange and its day-to-day fluctuations are analysed with respect to power-law tails as well long-term trends. We also model the transition to a Gaussian distribution for longer time intervals, like months instead of days.