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.
We empirically investigated the relationships between the degree of efficiency and the predictability in financial time-series data. The Hurst exponent was used as the measurement of the degree of efficiency, and the hit rate calculated from the nearest-neighbor prediction method was used for the prediction of the dire…
This letter investigates the dynamic relationship between market efficiency, liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin time series is anti-persistent. After 2013, as liquidity increased, the Hurst exponent ro…
Study examines how COVID-19 affected stock and crypto market efficiency.
This study investigates empirically whether the degree of stock market efficiency is related to the prediction power of future price change using the indices of twenty seven stock markets. Efficiency refers to weak-form efficient market hypothesis (EMH) in terms of the information of past price changes. The prediction …
Regularization is used to find a solution that both fits the data and is sufficiently smooth, and thereby is very effective for designing and refining learning algorithms. But the influence of its exponent remains poorly understood. In particular, it is unclear how the exponent of the reproducing kernel Hilbert space~(…
Study the link between entropy and market efficiency using fractal properties.
Python package for estimating Hurst exponent in fBm.
Study integrates implied Hurst exponent into IV models for better market efficiency.
Two-layer networks learn faster with batch reuse, overcoming information and leap exponents.
In this paper, three approaches to calculate the self-similarity exponent of a time series are compared in order to determine which one performs best to identify the transition from random efficient market behavior (EM) to herding behavior (HB) and hence, to find out the beginning of a market bubble. In particular, cla…
The study assesses how financial markets' efficiency changed during the COVID-19 crisis.
Study efficient estimation of hidden subspaces in Gaussian Multi-index models.
The state of a stochastic process evolving over a time is typically assumed to lie on a normal distribution whose width scales like . However, processes where the probability distribution is not normal and the scaling exponent differs from are known. The search for possible origins of such "a…
The market efficiency hypothesis has been proposed to explain the behavior of time series of stock markets. The Black-Scholes model (B-S) for example, is based on the assumption that markets are efficient. As a consequence, it is impossible, at least in principle, to "predict" how a market behaves, whatever the circums…
We report an empirical study of the Ibovespa index of the Sao Paulo Stock Exchange in which we detect the existence of long-range correlations. To analyze our data we introduce a rescaled variant of the usual Detrended Fluctuation Analysis that allows us to obtain the Hurst exponent through a one-parameter fitting. We …
Modeling financial markets as gas molecules, the paper predicts phase transitions similar to water and steam.
The total duration of drawdowns is shown to provide a moment-free, unbiased, efficient and robust estimator of Sharpe ratios both for Gaussian and heavy-tailed price returns. We then use this quantity to infer an analytic expression of the bias of moment-based Sharpe ratio estimators as a function of the return distrib…
Study shows a specific Carnot group violates a curvature exponent bound.
New groups found with critical exponents close to but less than max.
New learning rate approach reveals phase transitions in SGD performance.
Proposes a new metric for financial risk based on volatility's local deviations.
Kurdyka-Lojasiewicz (KL) exponent plays an important role in estimating the convergence rate of many contemporary first-order methods. In particular, a KL exponent of for a suitable potential function is related to local linear convergence. Nevertheless, KL exponent is in general extremely hard to estimate. I…
Study examines how Trump tariffs and COVID-19 affected financial market efficiency.
New proof for certain groups in higher dimensions.
New study shows non-adaptive trials can be outperformed by adaptive designs in treatment selection.
Extends Nash-Kuiper theorem to higher Hölder exponents.
In this paper, we show how the sampling properties of the Hurst exponent methods of estimation change with the presence of heavy tails. We run extensive Monte Carlo simulations to find out how rescaled range analysis (R/S), multifractal detrended fluctuation analysis (MF-DFA), detrending moving average (DMA) and genera…
Bi-Mamba model predicts diffusion coefficients and exponents from short data.
Study of deep neural networks using finite-time Lyapunov exponents.
Estimates roughness of volatility from discrete variance data.
Lyapunov exponents help understand RNN stability.
The condition for stationary increments, not scaling, detemines long time pair autocorrelations. An incorrect assumption of stationary increments generates spurious stylized facts, fat tails and a Hurst exponent H_s=1/2, when the increments are nonstationary, as they are in FX markets. The nonstationarity arises from s…
Study proves boundedness of operators in variable exponent Morrey spaces.
Proves critical exponent for positive representations in discrete subgroups.
Constructs free semigroups with critical exponents close to but less than ambient groups.
We study the asymptotic behavior of the Lyapunov exponent in a meromorphic family of random products of matrices in SL(2, C), as the parameter converges to a pole. We show that the blow-up of the Lyapunov exponent is governed by a quantity which can be interpreted as the non-Archimedean Lyapunov exponent of the family.…
This paper investigates the presence of long memory in corporate bond and stock indices of six European Union countries from July 1998 to February 2015. We compute the Hurst exponent by means of the DFA method and using a sliding window in order to measure long range dependence. We detect that Hurst exponents behave di…
Study critical exponents in normal subgroups of higher rank Lie groups.
In this paper we discuss a closed-form approximation of the likelihood functions of an arbitrary diffusion process. The approximation is based on an exponential ansatz of the transition probability for a finite time step , and a series expansion of the deviation of its logarithm from that of a Gaussian distribution…
New bounds on geodesic dimension and curvature exponent in Carnot groups.
Study approximates top Lyapunov exponents for surface mapping classes.
Study on curvature exponent of sub-Finsler Heisenberg groups, proving N_min ≥ 5.
We study the relationship between the Lyapunov exponents of the geodesic flow of a closed negatively curved manifold and the geometry of the manifold. We show that if each periodic orbit of the geodesic flow has exactly one Lyapunov exponent on the unstable bundle then the manifold has constant negative curvature. We a…
In this paper, we study the Kurdyka-Łojasiewicz (KL) exponent, an important quantity for analyzing the convergence rate of first-order methods. Specifically, we develop various calculus rules to deduce the KL exponent of new (possibly nonconvex and nonsmooth) functions formed from functions with known KL exponents. In …
Paper analyzes error exponent in agnostic PAC learning.
In previous work, the author fully classified orbit closures in genus three with maximally many (four) zero Lyapunov exponents of the Kontsevich-Zorich cocycle. In this paper, we prove that there are no higher dimensional orbit closures in genus three with any zero Lyapunov exponents. Furthermore, if a Teichmüller curv…
In the presence of a layer of metaprobabilities (from uncertainty concerning the parameters), the asymptotic tail exponent corresponds to the lowest possible tail exponent regardless of its probability. The problem explains "Black Swan" effects, i.e., why measurements tend to chronically underestimate tail contribution…
Study critical exponents on hyperbolic surfaces with long boundaries using Weil-Petersson measures.