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This paper analyzes approximately 100 Gigabytes of raw text data from Twitter with keywords “AAPL,” “S&P 500,” “FTSE100” and “NASDAQ” to explore the relationship between sentiment and the returns and prices on the Apple stock and the S&P 500, FTSE 100 and NASDAQ indices. The findings point to significant relationship and dependence between sentiment measures and the S&P 500 and FTSE 100 indices’ returns and prices. The econometric analysis of dependence between the aforementioned variables in the paper is presented in some detail for illustration of the methodology employed.

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.

© 2017 Elsevier B.V.The article presents the robust estimates of extreme movements and heavy-tailedness properties for Russian stock indices returns before and after sanctions were introduced. The obtained results show that almost for all sectoral indices there was a statistically significant increase in volatility. At the same time there is not enough evidence of structural breaks in heavy-tailedness, though some indications of heavier both right and left tails in the post-imposition period can be observed for some indices. However, we cannot with complete certainty directly link the increase in heavy-tailedness with the imposed sanctions. The latter to a considerable extent could be caused by higher country-specific risks due to geopolitical tensions as well as oil prices volatility. Whatever is the cause, any increases in heavy-tailedness can have grave consequences for corporate management, economic modeling and financial stability analysis.

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.

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.

We show that diversification does not reduce Value-at-Risk for a large class of dependent heavy tailed risks. The class is characterized by power law marginals with tail exponent no greater than one and by a general dependence structure which includes some of the most commonly used copulas.

Suppose estimating a model on each of a small number of potentially heterogeneous clusters yields approximately independent, unbiased, and Gaussian parameter estimators. We make two contributions in this setup. First, we show how to compare a scalar parameter of interest between treatment and control units using a two-sample t-statistic, extending previous results for the one-sample t-statistic. Second, we develop a test for the appropriate level of clustering; it tests the null hypothesis that clustered standard errors from a much finer partition are correct. We illustrate the approach by revisiting empirical studies involving clustered, time series, and spatially correlated data.

© 2017 The Author(s)This paper extends Ibragimov and Ibragimov (Econ Theory 32:579–587, 2007) in which the effect of changes income inequality on the price elasticity of market demand is characterized for the class of income distribution changes occurring through non-intersecting Lorenz curve shifts. We derive sufficient conditions for increase/decrease in price elasticity of market demand, under general changes in income distribution, allowing Lorenz curves to intersect as they shift. We conclude by drawing out implications of different types of tax policy changes for demand elasticity.

We develop new semiparametric bounds on the expected payoffs and prices of European call options and a wide range of path-dependent contingent claims. We first focus on the trinomial financial market model in which, as is well-known, an exact calculation of derivative prices based on no-arbitrage arguments is impossible. We show that the expected payoff of a European call option in the trinomial model with martingale-difference log-returns is bounded from above by the expected payoff of a call option written on an asset with i.i.d. symmetric two-valued log-returns. We further show that the expected payoff of a European call option in the multiperiod trinomial option pricing model is bounded by the expected payoff of a call option in the two-period model with a log-normal asset price. We also obtain bounds on the possible prices of call options in the (incomplete) trinomial model in terms of the parameters of the asset’s distribution. Similar bounds also hold for many other contingent claims in the trinomial option pricing model, including those with an arbitrary convex increasing payoff function as well as for path-dependent ones such as Asian options. We further obtain a wide range of new semiparametric moment bounds on the expected payoffs and prices of path-dependent Asian options with an arbitrary distribution of the underlying asset’s price. These results are based on recently obtained sharp moment inequalities for sums of multilinear forms and U-statistics and provide their first financial and economic applications in the literature. Similar bounds also hold for many other path-dependent contingent claims.

Excess volatility in main emerging and developed stock markets is carefully analysed in this study. Tail distribution of returns of both stock market index and individual stocks is evaluated and compared with the theoretical distribution found by Gabaix et al. (2003, 2006). For stock market index, recursive and rolling estimation are used. In recursive estimation, we find that all the developed markets obey “the Cubic Law of the Stock Returns”, while most of the emerging countries exhibit heavier tail with a tail index lower than 3 at 95% significance level. In rolling estimation, the tail index in the developed markets does not stabilise around 3, and after 2008 financial crisis, all the developed markets and most emerging ones suffer a drop in the tail index. For individual stocks, the tail distributions of stock returns, trading volume, and the number of trades in each emerging country behave quite differently from the theoretical model by Gabaix et al. (2006), especially the stock returns.

Focusing on the model of demand-driven innovation and spatial competition over time in Jovanovic and Rob (1987), we study the effects of the robustness of estimators employed by firms to make inferences about their markets on the firms’ growth patterns. We show that if consumers’ signals in the model are moderately heavy-tailed and the firms use the sample mean of the signals to estimate the ideal product, then the firms’ output levels exhibit positive persistence. In such a setting, large firms have an advantage over their smaller counterparts. These properties are reversed for signals with extremely heavy-tailed distributions. In such a case, the model implies anti-persistence in output levels, together with a surprising pattern of oscillations in firm sizes, with smaller firms being likely to become larger ones next period, and vice versa. We further show that the implications of the model under moderate heavy-tailedness continue to hold under the only assumption of symmetry of consumers’ signals if the firms use a more robust estimator of the ideal product, the sample median.

The wetlands of the Amudarya River delta in Uzbekistan provide valuable ecosystem services to the local human population which has suffered severely from the loss of the Aral Sea, desertification and the post-soviet socio-economic transition. The region is also particularly vulnerable to the impacts of climate change as a recent severe drought has shown. In this contribution, we assess the potential and implications of incorporating environmental flows into management of the Amudarya River for improving the provision of wetland ecosystem services and enhancing resilience of the social-ecological system to river runoff uncertainty. Our assessment is based on analyses of 1) the current vulnerability of deltaic wetlands to years of low water availability, 2) expected regional climate change and its impact on water flows to the wetlands, and 3) alternative water use options to enhance environmental flows under a changing climate. The results provide a ranking of these options with respect to their benefits for the provision of environmental flows and implications for agriculture. Their realization, however, poses challenges that cannot be tackled by technical interventions of redistribution and efficiency increase alone but call for institutional changes and moves towards multi-purpose water use. The diversification of impacts and livelihood options would allow enhancing the resilience of the social-ecological system to climate or socio-politically induced changes in water flow.

This article reports the efficiency of polymer-gellan as an oil displacement agent in comparison with water and polyacrylamide (PAM), which is traditionally used in the oil industry. The terrigenous and carbonate rocks used as core materials were characterized by scanning electron microscope. The porosity and permeability of the core materials were also determined. Sol-gel transition of polysaccharide-gellan in the presence of various salts was studied. It was found that the effectiveness of salts to enhance gelation follows this order: CaCl2 ≈ MgCl2 > KCl > NaCl. Influence of storage time and temperature on the viscosity of gellan was evaluated. Laboratory experiments on water flooding and polymer flooding methods were carried out on sand-packed model. Results of oil displacement experiments from sand-packed model and core samples were compared. It was shown that gellan and PAM show almost equal values of the oil displacement coefficient, which is 60–65%, while injection of water gives only 30–45%. Oil d...

The chapter discusses sharp probability and moment inequalities for random polynomials, generalized sample cross-moments, and their self-normalized and Studentized versions, in random variables (r.v.’s) with an arbitrary dependence. The results are based on sharp extensions of probability and moment inequalities for sums of independent r.v.’s to the case of the above statistics in independent symmetric variables. The case of statistics in dependent variables is treated through the use of measures of dependence. The results presented in this chapter are applicable in several settings in statistics, econometrics, and time series analysis, including tests for independence and problems of detecting nonlinear dependence.

© 2017 The Author(s)Motivated, in part, by the recent surge of interest in robust inequality measurement, cross-country inequality comparisons, applications of heavy-tailed distributions and the study of global and upper-tail inequality, this paper focuses on robust analysis of heavy-tailedness properties and inequality in the upper tails of income distribution in Russia, as measured, mainly, by its tail indices. The study is based on recently developed approaches to robust inference on the degree of heavy-tailedness and their implications for the analysis of upper-tail inequality discussed in the paper. Among other results, the paper provides robust estimates of heavy-tailedness parameters and tail indices for Russian income distribution and their comparisons with the benchmark values in developed economies reported in the previous literature. The estimates point out to important similarity between heavy-tailedness properties of income distribution and their implications for the analysis of upper-tail income inequality in Russia and those in developed markets.

© 2017 Elsevier B.V. The paper presents the robust estimates of tail indices for financial returns and returns asymmetry in the Russian stock market. We also investigate the relation between individual characteristics of companies and the degree of heavy-tailedness and asymmetry of returns. According to our estimates, the degree of heavy-tailedness is strongly related to the liquidity of stocks and the company size. At the same time, no significant effects on estimates of the tail indices of sectoral affiliation, cross-listing, adding into quotation lists, state ownership are revealed. As for the influence of the above-mentioned factors on the asymmetry of returns, the statistical reliability of relevant models is rather low. However, certain indicators of the asymmetry are observed for medium-sized regional companies, the majority showing a heavier right tail compared to the left tail. We also discuss the implications of our findings for managerial decisions and economic modeling. Our results may be useful for risk-managers, financial regulators, investors and policy-makers.

Okun’s law is a well-known relationship between the change in the unemployment rate and output growth. The main objective of this article is to provide a rigorous econometric analysis of Okun’s law for several CIS countries using different models and theoretically justified econometric methods. The traditional approach to Okun’s law estimation using OLS regressions does not account for possible endogeneity of regressors and the implied inconsistency of the estimates obtained. These problems point out to incorrectness of applications of the standard OLS estimation techniques. Our study addresses these issues by using econometrically justified instrumental variable regression methods. The article provides the results and discussions on practical use of Okun’s relationships for evaluation of average effects of economic growth on the unemployment rate, and vice versa; importance of accounting for confidence intervals in applications of Okun’s models to economic development analysis and cross-country comparisons and evaluation of effects of crises and other structural shocks on the economies considered. We also discuss in detail the results of formal econometric tests and economic motivation for validity of instrumental variables used in the study. The formal econometric tests, together with economic arguments, allow us to determine the most appropriate Okun-type models for each of the CIS countries under consideration.

We develop a general approach to robust inference about a scalar parameter of interest when the data is potentially heterogeneous and correlated in a largely unknown way. The key ingredient is the following result of Bakirov and Székely (2005) concerning the small sample properties of the standard t-test: For a significance level of 5% or lower, the t-test remains conservative for underlying observations that are independent and Gaussian with heterogenous variances. One might thus conduct robust large sample inference as follows: partition the data into q≥2 groups, estimate the model for each group, and conduct a standard t-test with the resulting q parameter estimators of interest. This results in valid and in some sense efficient inference when the groups are chosen in a way that ensures the parameter estimators to be asymptotically independent, unbiased and Gaussian of possibly different variances. We provide examples of how to apply this approach to time series, panel, clustered and spatially correlated data.

This paper presents an analysis of diversification and portfolio value at risk for heavy-tailed dependent risks in models with multiple common shocks. We show that, in the framework of value at risk comparisons, diversification is optimal for moderately heavy-tailed dependent risks with common shocks and finite first moments, provided that the model is balanced, i.e., that all the risks are available for portfolio formation. However, diversification is inferior in balanced extremely heavy-tailed risk models with common factors. Finally, in several unbalanced dependent models, diversification is optimal, even though there is extreme heavy-tailedness in common shocks or in idiosyncratic parts of the risks. Analogues of the obtained results further hold for efficiency comparisons of linear estimators in random effects models with dependent and heavy-tailed observations.

We study multiline insurance companies with limited liability and limited capital, creating the possibility of insurer default. Insurance premiums are determined by no-arbitrage option pricing methods. The results are developed under the realistic assumption that the losses created by insurer default are allocated among policyholders following an ex post, pro rata, sharing rule. In general, the ratio of default costs to expected claims, and thus the ratios of premiums to expected claims vary across insurance lines. Moreover, capital and related costs are allocated across lines in proportion to each line’s share of a digital default option on the insurer. Our results differ from those derived elsewhere in the literature.

We develop a framework for the optimal bundling problem of a multiproduct monopolist, who provides goods to consumers with private valuations that are random draws from a distribution with heavy tails. We show that in the Vickrey auction setting, the buyers prefer separate provision of the goods to any bundles. We also provide a complete characterization of the optimal bundling strategies for a monopolist producer, who provides goods for profit-maximizing prices. For products with low marginal costs, the seller's optimal strategy is to provide goods separately when consumers' valuations are heavy-tailed and in a single bundle when valuations are thin-tailed. These conclusions are reversed for goods with high marginal costs. For simplicity, we use a specific class of independent and identically distributed random variables, but our results can be generalized to include dependence, skewness, and the case of nonidentical one-dimensional distributions.

In this paper, we obtain characterizations of higher order Markov processes in terms of copulas corresponding to their finite-dimensional distributions. The results are applied to establish necessary and sufficient conditions for Markov processes of a given order to exhibitm-dependence,r-independence, or conditional symmetry. The paper also presents a study of applicability and limitations of different copula families in constructing higher order Markov processes with the preceding dependence properties. We further introduce new classes of copulas that allow one to combine Markovness withm-dependence orr-independence in time series.

We obtain estimates for the best constant in the Rosenthal inequality E | ∑ i = 1 n ξ i | 2 m ⩽ C ( 2 m ) max ( ∑ i = 1 n E ξ i 2 m , ( ∑ i = 1 n E ξ i 2 ) m ) for independent random variables ξ 1 , … , ξ n with l zero first odd moments, l ⩾ 1 . The estimates are sharp in the extremal cases l = 1 and l = m , that is, in the cases of random variables with zero mean and random variables with m zero first odd moments.

This paper presents a study of the intertemporal propagation of distributional properties of phenotypes in general polygenic multisex inheritance models with sex- and time-dependent heritabilities. It further analyzes the implications of these models under heavy-tailedness of traits' initial distributions. Our results suggest the optimality of a flexible asexual/binary mating system. Switching between asexual and binary inheritance mechanisms allows the population effectively to achieve a fast suppression of negative traits and a fast dispersion of positive traits, regardless of the distributional properties of the phenotypes in the initial period.

"Overall, the book is highly technical, including full mathematical proofs of the results stated. Potential readers are post-graduate students or researchers in Quantitative Risk Management willing to have a manual with the state-of-the-art on portfolio diversification and risk aggregation with heavy tails, including the fundamental theorems as well as collateral (but most useful) results on majorization and copula theory."

In this paper, we obtain sharp estimates for the expected payoffs and prices of European call options on an asset with an absolutely continuous price in terms of the price density characteristics. These techniques and results complement other approaches to the derivative pricing problem. Exact analytical solutions to option-pricing problems and to Monte-Carlo techniques make strong assumptions on the underlying asset's distribution. In contrast, our results are semi-parametric. This allows the derivation of results without knowing the entire distribution of the underlying asset's returns. Our results can be used to test different modelling assumptions. Finally, we derive bounds in the multiperiod binomial option-pricing model with time-varying moments. Our bounds reduce the multiperiod setup to a two-period setting, which is advantageous from a computational perspective.

This chapter demonstrates how majorization theory provides a powerful tool for the study of robustness of many important models in economics, finance, econometrics, statistics, risk management, and insurance to heavy-tailedness assumptions. The majorization relation is a formalization of the concept of diversity in the components of vectors. Over the past decades, majorization theory, which focuses on the study of this relation and functions that preserve it, has found applications in disciplines ranging from statistics, probability theory, and economics to mathematical genetics, linear algebra, and geometry (see Marshall et al. 2011, and the references therein).

Several approaches to the inference about the tail index ζ of heavy-tailed distributions are available in the literature (see, among others, the reviews in Beirlant et al. 2004; Embrechts et al. 1997). The two most commonly used ones are Hill’s estimator and the OLS approach using the log-log rank-size regression.

In this paper, we present a method that allows one to obtain a number of sharp inequalities for expectations of functions of infinite-degree U -statistics. Using the approach, we prove, in particular, the following result: Let D be the class of functions f : R+ → R+ such that the function f( x+ z) − f( x)is concave in x ∈ R+ for all z ∈ R+. Then the following estimate holds: Ef m

In this paper we prove analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal moment inequalities for symmetric statistics of arbitrary order in not identically distributed random variables. We also construct an example that shows the significance of each term in the obtained Rosenthal-type inequalities for symmetric statistics and obtain results concerning the rate of growth of the best constants in the inequalities.

We obtain an explicit representation for joint distribution of two-valued random variables with given marginals and for a copula corresponding to such random variables. The results are applied to prove a characterization of r-independent two-valued random variables in terms of their mixed first moments. The characterization is used to obtain an exact estimate for the number of almost independent random variables that can be defined on a discrete probability space and necessary conditions for a sequence of r-independent random variables to be stationary.

This paper presents the results of research aimed at improvement of the taxation of wages in Russia. It analysesthe problem of determining the progressive income tax scale as being a more socially equitable than the currentflat rate in Russia with 13% tax rate on income. Proposed tax scale of tax rates exempts the poor citizens fromincome tax, shifting the tax burden from the poor to the rich. In accordance with the principle of redistributionthat leads to a reduction in income inequality in Russia.The most important source of budget revenues are taxes. In Russia, as in most countries, the tax on personalincome (referred to as PIT) is one of the main sources of budget revenues. Its share of the budget is directlydependent on the level of economic development. This is one of the most popular taxes in the world payable onpersonal incomes. PIT is linked to consumption, and it can either stimulate consumption or reduce it. Therefore,the main challenge of income taxation is to achieve optimal balance between economic efficiency and socialjustice of the tax. In other words, such tax is required, which would provide the maximum equitableredistribution of income with minimal damage to the interests of taxpayers from taxation. Analysis of tax onpersonal income shows that it, as well as the whole tax system in the Russian Federation is constantlydeveloping.

In this article, the hydrodynamic behavior of dilute aqueous solutions of a natural polysaccharide—gellan in the porous media under the modeled oilfield conditions is described. The hydrodynamic properties of gellan and poly(acrylamide) solutions in saline porous media are compared. The influence of inorganic salts NaCl, KCl, CaCl2, MgCl2, and BaСl2 on sol–gel and gel–sol transitions of dilute gellan solutions was evaluated. The mechanism of sol–gel transition in the presence of individual alkaline and alkaline-earth metal salts is described on the basis of literature data. The viscometric measurements revealed that the effectiveness of salts to enhance gelation of gellan changes in the following order: BaСl2 > CaCl2 ≈ MgCl2 > KCl > NaCl. The sol–gel and gel–sol phase transitions of gellan solution were also observed upon addition of oil field water containing 73 g L−1 of alkaline and alkaline earth metal ions. During the injection of gellan solutions into the porous media saturated by saline water an oscillation of the injection pressure was observed. Such behavior of gellan is explained by either the sol-to-gel and the gel-to-sol transitions of the polymer taking place in saline water or the step-by-step plugging of high permeable channels until all high permeable channels of sand packs are plugged due to gellan invasion. The application of brine-initiated gelation of gellan for water shutoff operations (WSO) in field conditions was demonstrated. Higher technological effectiveness of gellan injection in comparison with existing gelation systems was shown. © 2014 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2015, 132, 41256.

In the present paper, we obtain the explicit expression for the best constant in the Rosenthal inequality for nonnegative random variables.

The present paper concentrates on the analogues of Rosenthal's inequalities for ordinary and decoupled bilinear forms in symmetric random variables. More specifically, we prove the exact moment inequalities for these objects in terms of moments of their individual components. As a corollary of these results we obtain the explicit expressions for the best constant in the analogues of Rosenthal's inequality for ordinary and decoupled bilinear forms in identically distributed symmetric random variables in the case of the fixed number of random variables.

In this paper we prove the analogues of Khintchine, Marcinkiewicz-Zygmund and Rosenthal moment inequalities for symmetric statistics of second order in not identically distributed random variables.