arXiv subjects

Rustam Ibragimov

Publications and source records attributed to Rustam Ibragimov.

6 recordsLinked to original sources

arXiv2025

Robust Cauchy-Based Methods for Predictive Regressions

This paper develops robust inference methods for predictive regressions that address key challenges posed by endogenously persistent or heavy-tailed regressors, as well as persistent volatility in errors. Building on the Cauchy estimation framework, we propose two novel tests: one based on $t$-statistic group inference and the other employing a hybrid approach that combines Cauchy and OLS estimation. These methods effectively mitigate size distortions that commonly arise in standard inference procedures under endogeneity, near nonstationarity, heavy tails, and persistent volatility. The proposed tests are simple to implement and applicable to both continuous- and discrete-time models. Extensive simulation experiments demonstrate favorable finite-sample performance across a range of realistic settings. An empirical application examines the predictability of excess stock returns using the dividend-price and earnings-price ratios as predictors. The results suggest that the dividend-price ratio possesses predictive power, whereas the earnings-price ratio does not significantly forecast returns.

econ.EM↗

arXiv2021

Robust Inference on Income Inequality: $t$-Statistic Based Approaches

Empirical analyses on income and wealth inequality and those in other fields in economics and finance often face the difficulty that the data is heterogeneous, heavy-tailed or correlated in some unknown fashion. The paper focuses on applications of the recently developed \textit{t}-statistic based robust inference approaches in the analysis of inequality measures and their comparisons under the above problems. Following the approaches, in particular, a robust large sample test on equality of two parameters of interest (e.g., a test of equality of inequality measures in two regions or countries considered) is conducted as follows: The data in the two samples dealt with is partitioned into fixed numbers $q_1, q_2\ge 2$ (e.g., $q_1=q_2=2, 4, 8$) of groups, the parameters (inequality measures dealt with) are estimated for each group, and inference is based on a standard two-sample $t-$test with the resulting $q_1, q_2$ group estimators. Robust $t-$statistic approaches result in valid inference under general conditions that group estimators of parameters (e.g., inequality measures) considered are asymptotically independent, unbiased and Gaussian of possibly different variances, or weakly converge, at an arbitrary rate, to independent scale mixtures of normal random variables. These conditions are typically satisfied in empirical applications even under pronounced heavy-tailedness and heterogeneity and possible dependence in observations. The methods dealt with in the paper complement and compare favorably with other inference approaches available in the literature. The use of robust inference approaches is illustrated by an empirical analysis of income inequality measures and their comparisons across different regions in Russia.

econ.EM↗

arXiv2021

COVID-19: Tail Risk and Predictive Regressions

The paper focuses on econometrically justified robust analysis of the effects of the COVID-19 pandemic on financial markets in different countries across the World. It provides the results of robust estimation and inference on predictive regressions for returns on major stock indexes in 23 countries in North and South America, Europe, and Asia incorporating the time series of reported infections and deaths from COVID-19. We also present a detailed study of persistence, heavy-tailedness and tail risk properties of the time series of the COVID-19 infections and death rates that motivate the necessity in applications of robust inference methods in the analysis. Econometrically justified analysis is based on heteroskedasticity and autocorrelation consistent (HAC) inference methods, recently developed robust $t$-statistic inference approaches and robust tail index estimation.

econ.EM↗

arXiv2020

New Approaches to Robust Inference on Market (Non-)Efficiency, Volatility Clustering and Nonlinear Dependence

Many financial and economic variables, including financial returns, exhibit nonlinear dependence, heterogeneity and heavy-tailedness. These properties may make problematic the analysis of (non-)efficiency and volatility clustering in economic and financial markets using traditional approaches that appeal to asymptotic normality of sample autocorrelation functions of returns and their squares. This paper presents new approaches to deal with the above problems. We provide the results that motivate the use of measures of market (non-)efficiency and volatility clustering based on (small) powers of absolute returns and their signed versions. We further provide new approaches to robust inference on the measures in the case of general time series, including GARCH-type processes. The approaches are based on robust $t-$statistics tests and new results on their applicability are presented. In the approaches, parameter estimates (e.g., estimates of measures of nonlinear dependence) are computed for groups of data, and the inference is based on $t-$statistics in the resulting group estimates. This results in valid robust inference under heterogeneity and dependence assumptions satisfied in real-world financial markets. Numerical results and empirical applications confirm the advantages and wide applicability of the proposed approaches.

econ.EM↗

arXiv2020

New robust inference for predictive regressions

We propose two robust methods for testing hypotheses on unknown parameters of predictive regression models under heterogeneous and persistent volatility as well as endogenous, persistent and/or fat-tailed regressors and errors. The proposed robust testing approaches are applicable both in the case of discrete and continuous time models. Both of the methods use the Cauchy estimator to effectively handle the problems of endogeneity, persistence and/or fat-tailedness in regressors and errors. The difference between our two methods is how the heterogeneous volatility is controlled. The first method relies on robust t-statistic inference using group estimators of a regression parameter of interest proposed in Ibragimov and Muller, 2010. It is simple to implement, but requires the exogenous volatility assumption. To relax the exogenous volatility assumption, we propose another method which relies on the nonparametric correction of volatility. The proposed methods perform well compared with widely used alternative inference procedures in terms of their finite sample properties.

econ.EM↗

arXiv2006

Characterizations of joint distributions, copulas, information, dependence and decoupling, with applications to time series

In this paper, we obtain general representations for the joint distributions and copulas of arbitrary dependent random variables absolutely continuous with respect to the product of given one-dimensional marginal distributions. The characterizations obtained in the paper represent joint distributions of dependent random variables and their copulas as sums of $U$-statistics in independent random variables. We show that similar results also hold for expectations of arbitrary statistics in dependent random variables. As a corollary of the results, we obtain new representations for multivariate divergence measures as well as complete characterizations of important classes of dependent random variables that give, in particular, methods for constructing new copulas and modeling different dependence structures. The results obtained in the paper provide a device for reducing the analysis of convergence in distribution of a sum of a double array of dependent random variables to the study of weak convergence for a double array of their independent copies. Weak convergence in the dependent case is implied by similar asymptotic results under independence together with convergence to zero of one of a series of dependence measures including the multivariate extension of Pearson's correlation, the relative entropy or other multivariate divergence measures. A closely related result involves conditions for convergence in distribution of $m$-dimensional statistics $h(X_t,X_{t+1},...,X_{t+m-1})$ of time series $\{X_t\}$ in terms of weak convergence of $h(ξ_t,ξ_{t+1},...,ξ_{t+m-1})$, where $\{ξ_t\}$ is a sequence of independent copies of $X_t'$s, and convergence to zero of measures of intertemporal dependence in $\{X_t\}$. The tools used include new sharp estimates for the distance between the distribution function of an arbitrary statistic in dependent random variables and the distribution function of the statistic in independent copies of the random variables in terms of the measures of dependence of the random variables. Furthermore, we obtain new sharp complete decoupling moment and probability inequalities for dependent random variables in terms of their dependence characteristics.

math.ST↗