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.
SignSGD outperforms SGD in linear regression with optimal scaling laws under PLRF model.
The paper presents a multi-power law for predicting loss curves across different learning rate schedules.
We study by theoretical analysis and by direct numerical simulation the dynamics of a wide class of asynchronous stochastic systems composed of many autocatalytic degrees of freedom. We describe the generic emergence of truncated power laws in the size distribution of their individual elements. The exponents of the…
We focus on emergence of the power-law cross-correlations from processes with both short and long term memory properties. In the case of correlated error-terms, the power-law decay of the cross-correlation function comes automatically with the characteristics of separate processes. Bivariate Hurst exponent is then equa…
We discover scaling laws for kernel regression loss under various learning rate schedules.
The persistence phenomenon is studied in the Japanese financial market by using a novel mapping of the time evolution of the values of shares quoted on the Nikkei Index onto Ising spins. The method is applied to historical end of day data from the Japanese stock market during 2002. By studying the time dependence of th…
We study the relaxation dynamics of a financial market just after the occurrence of a crash by investigating the number of times the absolute value of an index return is exceeding a given threshold value. We show that the empirical observation of a power law evolution of the number of events exceeding the selected thre…
New model explains volatility after extreme stock market events.
Power-law spectrum of random feature model is preserved in neural networks.
We explain theoretically a curious empirical phenomenon: "Approximating a matrix by deterministically selecting a subset of its columns with the corresponding largest leverage scores results in a good low-rank matrix surrogate". To obtain provable guarantees, previous work requires randomized sampling of the columns wi…
Study on KRR with power-law data, showing better sample complexity.
Stochastic block models (SBMs) have been playing an important role in modeling clusters or community structures of network data. But, it is incapable of handling several complex features ubiquitously exhibited in real-world networks, one of which is the power-law degree characteristic. To this end, we propose a new var…
Estimates self- and cross-impact concavity and decay patterns in financial markets.
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 …
Optimal learning rates decay to zero in easy tasks and maintain a warmup phase in hard tasks.
The relaxation dynamics of aftershocks after large volatility shocks are investigated based on two high-frequency data sets of the Shanghai Stock Exchange Composite (SSEC) index. Compared with previous relevant work, we have defined main financial shocks based on large volatilities rather than large crashes. We find th…
The quotient of random variables with normal distributions is examined and proven to have have power law decay, with density , with the coefficient depending on the means and variances of the numerator and denominator and their correlation. We also obtain the conditional probability…
The study uses the Merton model to estimate PD and finds a phase transition affecting convergence speed.
New mechanism found for power laws including Zipf's law.
Stock prices are observed to be random walks in time despite a strong, long term memory in the signs of trades (buys or sells). Lillo and Farmer have recently suggested that these correlations are compensated by opposite long ranged fluctuations in liquidity, with an otherwise permanent market impact, challenging the s…
Study classifies stock price jumps as exogenous or endogenous using news data.
We analyze a database comprising quarterly sales of 55624 pharmaceutical products commercialized by 3939 pharmaceutical firms in the period 1992--2001. We study the probability density function (PDF) of growth in firms and product sales and find that the width of the PDF of growth decays with the sales as a power law w…
We respond to the issues discussed by Farmer and Lillo (FL) related to our proposed approach to understanding the origin of power-law distributions in stock price fluctuations. First, we extend our previous analysis to 1000 US stocks and perform a new estimation of market impact that accounts for splitting of large ord…
Study shows how anisotropic data affects learning dynamics in phase retrieval.
Optimal trading strategy derived for nonlinear price impact models.
A hierarchical model shows how scaling laws emerge from sequential feature recovery.
We compare systematically several classes of stochastic volatility models of stock market fluctuations. We show that the long-time return distribution is either Gaussian or develops a power-law tail, while the short-time return distribution has generically a stretched-exponential form, but can assume also an algebraic …
We study soft persistence (existence in subsequent temporal layers of motifs from the initial layer) of motif structures in Triangulated Maximally Filtered Graphs (TMFG) generated from time-varying Kendall correlation matrices computed from stock prices log-returns over rolling windows with exponential smoothing. We ob…
We show power-scaling behaviors for fluctuations in share volume, which no other studies have so far done. After analyzing a database of the daily transactions for all securities listed on the Tokyo Stock Exchange, we selected 1050 large companies that each had an unbroken series of daily trading activity from January …
We model the arrival of mid-price changes in the E-Mini S&P futures contract as a self-exciting Hawkes process. Using several estimation methods, we find that the Hawkes kernel is power-law with a decay exponent close to -1.15 at short times, less than approximately 10^3 seconds, and crosses over to a second power-law …
We analyze the memory in volatility by studying volatility return intervals, defined as the time between two consecutive fluctuations larger than a given threshold, in time periods following stock market crashes. Such an aftercrash period is characterized by the Omori law, which describes the decay in the rate of after…
Polynomial decay of correlations shown for curved surfaces.
The bitcoin price has surged in recent years and it has also exhibited phases of rapid decay. In this paper we address the question to what extent this novel cryptocurrency market can be viewed as a classic or semi-efficient market. Novel and robust tools for estimation of multi-fractal properties are used to show that…
Second part of series studying charged scalar fields on Reissner--Nordström spacetimes.
This article provides a novel framework to evaluate limit order tactics that highlights expected fill price, adverse price selection cost, and opportunity cost. We formulate the problem of optimal execution of market orders with nonlinear market impact, power law decay kernel, and stochastic and deterministic liquidity…
We study the statistical properties of volatility---a measure of how much the market is likely to fluctuate. We estimate the volatility by the local average of the absolute price changes. We analyze (a) the S&P 500 stock index for the 13-year period Jan 1984 to Dec 1996 and (b) the market capitalizations of the largest…
TDA detects financial bubbles through early warning signals.
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. In recent empirical studies of stock market indices it was examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Levy-stable distribution L_{alpha}(r)…
Detection of power-law behavior and studies of scaling exponents uncover the characteristics of complexity in many real world phenomena. The complexity of financial markets has always presented challenging issues and provided interesting findings, such as the inverse cubic law in the tails of stock price fluctuation di…
The three-state agent-based 2D model of financial markets as proposed by Giulia Iori has been extended by introducing increasing trust in the correctly predicting agents, a more realistic consultation procedure as well as a formal validation mechanism. This paper shows that such a model correctly reproduces the three f…
Gradient descent outperforms ridge regression under certain covariance matrix decay conditions.
Analyzed Bitcoin market index volatility changes over two distinct periods using anomalous diffusion and multifractal analysis.
Bayesian inference and superstatistics model financial volatility dynamics across different timescales.
In this study we examine the evolution of price, volume, and the bid-ask spread after extreme 15 minute intraday price changes on the NYSE and the NASDAQ. We find that due to strong behavioral trading there is an overreaction. Furthermore we find that volatility which increases sharply at the event decays according to …
We address the problem of long-range memory in the financial markets. There are two conceptually different ways to reproduce power-law decay of auto-correlation function: using fractional Brownian motion as well as non-linear stochastic differential equations. In this contribution we address this problem by analyzing e…
Recent empirical studies have demonstrated long-memory in the signs of orders to buy or sell in financial markets [2, 19]. We show how this can be caused by delays in market clearing. Under the common practice of order splitting, large orders are broken up into pieces and executed incrementally. If the size of such lar…
We discuss the distribution of commuting distances and its relation to income. Using data from Denmark, the UK, and the US, we show that the commuting distance is (i) broadly distributed with a slow decaying tail that can be fitted by a power law with exponent and (ii) an average growing slowly as a power …
Study on SGD dynamics and scaling laws for training quadratic neural networks in high dimensions.