arXiv subjects

Andrey Sarantsev

Publications and source records attributed to Andrey Sarantsev.

At least 19 recordsLinked to original sources

arXiv2026

Modeling Stock Returns and Volatility Using Bivariate Gamma Generalized Laplace Law

We consider a generalization of the variance-gamma (generalized asymmetric Laplace) distribution, defined as a normal mean - variance mixture with a gamma mixing distribution. While this model is typically studied in the univariate setting, we assume that the gamma mixing variable is observed alongside the primary variable, resulting in a bivariate framework. In this setting, maximum likelihood estimation becomes significantly simpler than in the standard univariate case, reducing to a form of classical linear regression. We derive explicit expressions for the resulting estimators. For certain parameter configurations, the estimators exhibit nonstandard convergence rates, exceeding the usual square-root rate. Finally, we illustrate the applicability of this model in financial contexts by analyzing stock index returns and associated volatility for several major indices.

stat.ME↗

arXiv2026

Fast Convergence for Weighted Least Squares Estimates

It is well-known that maximum likelihood estimates converge faster than the classic square root rate if the Fisher information is infinite. This is often the case when the effective region depends on the estimated parameters, or when density has a singularity inside the effective region at a point dependent on the estimated parameters. We present a one-parameter family of bivariate absolutely continuous distributions on the half-space with smooth densities. The effective domain is always the same half-space and does not depend on this parameter. The order of magnitude for the weighted least squares estimate is asymptotically smaller than the classic square root rate. For the Gaussian variance mixture case, the maximum likelihood estimate coincides with this weighted least squares estimate.

math.ST↗

arXiv2026

Random Stability of Random Variables

For a random variable $N = 0, 1, 2, \ldots$ we study the following question: When does the sum of $N$ many independent and identically distributed copies of a random variable $X$ have the same law a a nontrivial rescaling of $X$? We show that such $N$-stable random variable exists if and only $1 < \mathbb E[N] < \infty$. Under an additional assumption $\mathbb E[N\ln N] < \infty$, we describe all $N$-stable $X$. We also study a converse problem: For a given $X \ge 0$ with $\mathbb E[X] = 1$, we study the set of all $N$ such that $X$ is $N$-stable. Distributions of $N$ form a semigroup with respect to composition of probability generating functions. We show these probability generating functions need to commute with respect to composition. We present explicit families of composition semigroups. Equivalent formulations have appeared in difference forms, and this article aims to unify and extend them.

math.PR↗

arXiv2026

GPS constellation search for exotic physics messengers coincident with the binary neutron star merger GW170817

The Global Positioning System (GPS) includes a continuously operating, planet-scale network of atomic clocks that, beyond navigation and time dissemination, enables precision tests of fundamental physics. Here we use GPS carrier phase archival data to perform a retrospective search for exotic low-mass fields (ELFs) that might be emitted by the binary neutron-star merger GW170817, complementing gravitational wave and electromagnetic modalitiesnin multi-messenger astronomy. Such ultra-relativistic fields would imprint a dispersive, anti-chirp signature in clock-frequency time series, delayed with respect to the LIGO-Virgo gravitational wave detection. We construct network-median pseudo-frequency data from eighteen Rb satellite clocks referenced to a terrestrial hydrogen maser and conduct a template-bank search spanning ELF pulse duration, arrival delay, and characteristic frequency. No statistically significant signal is observed after accounting for noise statistics and template-bank trials. We derive 95\% confidence-level lower bounds on the interaction energy scale $\Lambda_\alpha$ of quadratic couplings driving variations in electromagnetic fine-structure constant. These limits improve upon existing astrophysical and gravity-test constraints across the ELF-energy range $\approx10^{-18}$--$10^{-14}\,\mathrm{eV}$. This demonstrates that mature global satellite-clock networks provide an observational capability for retrospective, multi-messenger searches for new physics using decades of archival timing data.

astro-ph.IM↗

arXiv2025

Valuation Measure of the Stock Market using Stochastic Volatility and Stock Earnings

We create a time series model for annual returns of three asset classes: the USA Standard & Poor (S&P) stock index, the international stock index, and the USA Bank of America investment-grade corporate bond index. Using this, we made an online financial app simulating wealth process. This includes options for regular withdrawals and contributions. Four factors are: S&P volatility and earnings, corporate BAA rate, and long-short Treasury bond spread. Our valuation measure is an improvement of Shiller's cyclically adjusted price-earnings ratio. We use classic linear regression models, and make residuals white noise by dividing by annual volatility. We use multivariate kernel density estimation for residuals. We state and prove long-term stability results.

q-fin.RM↗

arXiv2024

Capital Asset Pricing Model with Size Factor and Normalizing by Volatility Index

The Capital Asset Pricing Model (CAPM) relates a well-diversified stock portfolio to a benchmark portfolio, usually taken to be the S\&P 500. We insert size effect in the CAPM, capturing a real-life feature that on average, small stocks (measured by market capitalization) have higher risk and return than large stocks. Testing CAPM involves fitting linear regressions. Our goal is to ensure that regression residuals are independent identically distributed Gaussian. In some cases, we find that including the Volatility Index as a multiplicative factor by these residuals makes them closer to that ideal. In this article, we combine these ideas to create a new discrete-time model, which includes volatility, size factor, and the CAPM. We fit this model using real-world data, prove the long-term stability of this model, and analyze the resulting capital distribution curves.

q-fin.MF↗

arXiv2024

Zero-Coupon Treasury Rates and Returns using the Volatility Index

We study a multivariate autoregressive stochastic volatility model for the first 3 principal components (level, slope, curvature) of 10 series of zero-coupon Treasury bond rates with maturities from 1 to 10 years. We fit this model using monthly data from 1990. Unlike classic models with hidden stochastic volatility, here it is observed as VIX: the volatility index for the S&P 500 stock market index. Surprisingly, this stock index volatility works for Treasury bonds, too. Next, we prove long-term stability and the Law of Large Numbers. We express total returns of zero-coupon bonds using these principal components. We prove the Law of Large Numbers for these returns. All results are done for discrete and continuous time.

q-fin.ST↗

arXiv2024

Log Heston Model for Monthly Average VIX

We model time series of VIX (monthly average) and monthly stock index returns. We use log-Heston model: logarithm of VIX is modeled as an autoregression of order 1. Our main insight is that normalizing monthly stock index returns (dividing them by VIX) makes them much closer to independent identically distributed Gaussian. The resulting model is mean-reverting, and the innovations are non-Gaussian. The combined stochastic volatility model fits well, and captures Pareto-like tails of real-world stock market returns. This works for small and large stock indices, for both price and total returns.

q-fin.ST↗

arXiv2024

New Time Series Models for Corporate Bond Log Yields

We propose a class of simple time series models for rates and spreads of portfolios of corporate bonds classified by ratings provided by Bank of America. We evaluate these models based on statistical analysis of innovations: Whether they are independent identically distributed. Our tests are unusually rigorous, compared with standard practice, Our novelty is taking logarithms of rates or spreads instead of rates or spreads themselves. We find out that the best option is to take logarithms of spreads of logarithms of rates. Sometimes, dividing these innovations by the volatility index for stocks makes them pass our statistical tests. It is remarkable that stock volatility can also serve as bond volatility.

q-fin.ST↗

arXiv2024

Tutorial on running median subtraction filter with application to searches for exotic field transients in multi-messenger astronomy

Running Median Subtraction Filter (RMSF) is a robust statistical tool for removing slowly varying baselines in data streams containing transients (short-duration signals) of interest. In this work, we explore the RMSF performance and properties using simulated time series and analytical methods. We study the RMSF fidelity in preserving the signal of interest in the data using (i) a Gaussian pulse and (ii) a transient oscillatory signal. Such signals may be generated by hypothetical exotic low-mass fields (ELFs) associated with intense astrophysical events like binary black hole or neutron star mergers. We consider and assess RMSF as a candidate method to extract transient ELF signals. RMSF operates by sliding a window across the data and subtracting the median value within each window from the data points. With a suitable choice of running window size, RMSF effectively filters out baseline variations without compromising the integrity of transients. The RMSF window width is a critical parameter: it must be wide enough to encompass a short transient but narrow enough to remove the slowly varying baseline. We show that the RMSF removes the mean of a normally distributed white noise while preserving its variance and higher order moments in the limit of large windows. In addition, RMSF does not color the white noise stream, i.e., it does not induce any significant correlation in the filtered data. Ideally, a filter would preserve both the signal of interest and the statistical characteristics of the stochastic component of the data, while removing the background clutter and outliers. We find the RMSF to satisfy these practical criteria for data pre-processing. While we rigorously prove several RMSF properties, the paper is organized as a tutorial with multiple illustrations of RMSF applications.

astro-ph.IM↗

arXiv2023

Modified Method of Moments for Generalized Laplace Distribution

In this note, we consider the performance of the classic method of moments for parameter estimation of symmetric variance-gamma (generalized Laplace) distributions. We do this through both theoretical analysis (multivariate delta method) and a comprehensive simulation study with comparison to maximum likelihood estimation, finding performance is often unsatisfactory. In addition, we modify the method of moments by taking absolute moments to improve efficiency; in particular, our simulation studies demonstrate that our modified estimators have significantly improved performance for parameter values typically encountered in financial modelling, and is also competitive with maximum likelihood estimation.

stat.ME↗

arXiv2023

Boundary Approximation for Sticky Jump-Reflected Processes on the Half-Line

The Skorokhod reflection was used in 1961 to create a reflected diffusion on the half-line. Later, it was used for processes with jumps such as reflected Lévy processes. Like a Brownian motion, which is a weak limit of random walks, reflected processes on the half-line serve as weak limits of random walks with switching regimes at zero: one regime away from zero, the other around zero. In this article, we develop a general theory of this regime change and prove convergence to a function with generalized reflection. Our results are deterministic and can be applied to a wide class of stochastic processes. Applications include storage processes, heavy traffic limits, diffusion on a half-line with a combination of continuous reflection, jump exit, and a delay at 0.

math.PR↗

arXiv2023

The Variance-Gamma Distribution: A Review

The variance-gamma (VG) distributions form a four-parameter family which includes as special and limiting cases the normal, gamma and Laplace distributions. Some of the numerous applications include financial modelling and distributional approximation on Wiener space. In this review, we provide an up-to-date account of the basic distributional theory of the VG distribution. Properties covered include probability and cumulative distribution functions, generating functions, moments and cumulants, mode and median, Stein characterisations, representations in terms of other random variables, and a list of related distributions. We also review methods for parameter estimation and some applications of the VG distribution, including the aforementioned applications to financial modelling and distributional approximation on Wiener space.

math.ST↗

arXiv2022

Birth and Death Processes in Interactive Random Environments

This paper studies birth and death processes in interactive random environments where the birth and death rates and the dynamics of the state of the environment are dependent on each other. Two models of a random environment are considered: a continuous-time Markov chain (finite or countably infinite) and a reflected (jump) diffusion process. The background is determined by a joint Markov process carrying a specific interactive mechanism, with an explicit invariant measure whose structure is similar to a product form. We discuss a number of queueing and population-growth models and establish conditions under which the above-mentioned invariant measure can be derived. Next, an analysis of the rate of convergence to stationarity is performed for the models under consideration. We consider two settings leading to either an exponential or a polynomial convergence rate. In both cases we assume that the underlying environmental Markov process has an exponential rate of convergence, but the convergence rate of the joint Markov process is determined by certain conditions on the birth and death rates. To prove these results a coupling method turns out to be useful.

math.PR↗

arXiv2022

IID Time Series Testing

Traditional white noise testing, for example the Ljung-Box test, studies only the autocorrelation function (ACF). Time series can be heteroscedastic and therefore not i.i.d. but still white noise (that is, with zero ACF). An example of heteroscedasticity is financial time series: times of high variance (financial crises) can alternate with times of low variance (calm times). Here, absolute values of time series terms are not white noise. We could test for white noise separately for original and absolute values, for example using Ljung-Box tests for both. In this article, we create an omnibus test which combines these two tests. Moreover, we create a general framework to create various i.i.d. tests. We apply tests to simulated data, both autoregressive linear and heteroscedastic.

math.ST↗

arXiv2021

Penalty Method for Obliquely Reflected Diffusions

Take a multidimensional normally or obliquely reflected diffusion in a smooth domain. Approximate it by solutions of stochastic differential equations without reflection using the penalty method. That is, we approximate the reflection term with an additional drift term. In the existing literature, usually a specific approximating sequence is provided in order to prove existence of a reflected diffusion. In this article, we provide general sufficient conditions on the approximating coefficients.

math.PR↗

arXiv2021

Optimal Portfolio with Power Utility of Absolute and Relative Wealth

Portfolio managers often evaluate performance relative to benchmark, usually taken to be the Standard & Poor 500 stock index fund. This relative portfolio wealth is defined as the absolute portfolio wealth divided by wealth from investing in the benchmark (including reinvested dividends). The classic Merton problem for portfolio optimization considers absolute portfolio wealth. We combine absolute and relative wealth in our new utility function. We also consider the case of multiple benchmarks. To both absolute and relative wealth, we apply power utility functions, possibly with different exponents. We obtain an explicit solution and compare it to the classic Merton solution. We apply our results to the Capital Asset Pricing Model setting.

q-fin.PM↗

arXiv2021

Beam-spin asymmetry $\boldsymbolΣ$ for $Σ^-$ hyperon photoproduction off the neutron

We report a new measurement of the beam-spin asymmetry $\boldsymbolΣ$ for the $\vecγ n \rightarrow K^+Σ^-$ reaction using quasi-free neutrons in a liquid-deuterium target. The new dataset includes data at previously unmeasured photon energy and angular ranges, thereby providing new constraints on partial wave analyses used to extract properties of the excited nucleon states. The experimental data were obtained using the CEBAF Large Acceptance Spectrometer (CLAS), housed in Hall B of the Thomas Jefferson National Accelerator Facility (JLab). The CLAS detector measured reaction products from a liquid-deuterium target produced by an energy-tagged, linearly polarised photon beam with energies in the range 1.1 to 2.3 GeV. Predictions from an isobar model indicate strong sensitivity to $N(1720)3/2^+$, $Δ(1900)1/2^-$, and $N(1895)1/2^-$, with the latter being a state not considered in previous photoproduction analyses. When our data are incorporated in the fits of partial-wave analyses, one observes significant changes in $γ$-$n$ couplings of the resonances which have small branching ratios to the $πN$ channel.

nucl-ex↗