Thick Tails Research Articles

Ethereum futures and the efficiency of cryptocurrency spot markets

This paper examines the impact of the introduction of Ethereum futures contracts on the market efficiency of major cryptocurrency (Bitcoin, Ethereum, Ripple, Litecoin, and Dogecoin) spot prices. Using a multifractality-based approach and daily data from September 4, 2017 to February 16, 2024, the main results show a slight improvement in market efficiency. Specifically, the degree of multifractality persistence decreases, implying reduced market inefficiencies in major cryptocurrencies. The temporal linear correlation effect and thick tail effect are less pronounced post-launch. The asymmetry of the generalized Hurst exponent increases after the launch of Ethereum futures, with a higher persistence under the downward trend of cryptocurrencies noted. This downward trend emerges after the launch of Ethereum futures, coinciding with the final stage of the COVID-19 pandemic. Additional analysis shows that fat tails and temporal linear correlations are the main sources of multifractality. The results highlight the influence of introducing financial derivatives into the relatively new and volatile cryptocurrency area, which should concern traders, hedgers, investors, and regulators.

Consumption dynamics and welfare under non-Gaussian earnings risk

Recent empirical studies document that the distribution of earnings changes displays substantial deviations from lognormality: in particular, earnings changes are negatively skewed with extremely high kurtosis (long and thick tails), and these non-Gaussian features vary substantially both over the life cycle and with the earnings level of individuals. Furthermore, earnings changes display nonlinear (asymmetric) mean reversion. In this paper, we embed a very rich “benchmark earnings process” that captures these non-Gaussian and nonlinear features into a lifecycle consumption-saving model and study its implications for consumption dynamics, consumption insurance, and welfare. We show four main results. First, the benchmark process essentially matches the empirical lifetime earnings inequality—a first-order proxy for consumption inequality—whereas the canonical Gaussian (persistent-plus-transitory) process understates it by a factor of five to ten. Second, the welfare cost of idiosyncratic risk implied by the benchmark process is between two-to-four times higher than the canonical Gaussian one. Third, the standard method in the literature for measuring the pass-through of income shocks to consumption—can significantly overstate the degree of consumption smoothing possible under non-Gaussian shocks. Fourth, the marginal propensity to consume out of transitory income (e.g., from a stimulus check) is higher under non-Gaussian earnings risk.

An endogenous evolution mechanism model of asset prices based on time-varying risk aversion coefficient

In the traditional heterogeneous agent model, investors are assumed to be risk averse, and the wealth expected utility function maximization principle is used to form the optimal asset quantity demand. In such models, the risk aversion coefficient of investors is often assumed to be constant. This paper considers that the risk aversion coefficient of investors is time-varying and changes with the change of wealth, and establishes an endogenous evolutionary mechanism model formed by fundamental analysts, technical analysts, and market makers. Compared with the fixed risk aversion coefficient model, this paper analyzes the investor’s behavior, the interaction between investor behaviors, and the influence of different types of investors on the stability of the market. At the same time, we test asset price and asset behavior and conclude that investor behavior affects the stability of the system model. The numerical simulation of the corresponding stochastic model shows that the model can simulate the basic characteristics of financial time series, such as the partial peak and thick tail of asset return series, and the long memory of fluctuations.

Small‐sample properties of robust willingness‐to‐pay estimators

AbstractThe small‐sample properties of robust, binary choice willingness‐to‐pay (WTP) estimators are analyzed. A Monte Carlo simulation compares the bias and mean‐squared error of marginal and expected WTP estimates from probit, zero‐centered (“robit”), logit, and a generalized Tukey lambda distribution called a “pregibit” regression under normal and nonnormal distributional assumptions. Robust binary choice estimators allow for variation in tail thickness (the robit and pregibit) or tail asymmetry (the pregibit). No previous studies have compared the performance of these WTP estimators. The findings will interest researchers who use contingent validation methods to estimate WTP for nonmarket or hypothetical goods.

Sexual Dimorphism of Shell Turtles (Cuora amboinensis) in the Ex-situ Conservation Area, Bengkulu University, Sumatra

This research aims to determine the physical differences between male and female turtles based on the secondary morphological characteristics of Cuora amboinensis. The method used in this research is a visual method with metric data presented in photos and measurement data, with a sample size of 20 individuals consisting of 12 females and 8 males. The research was carried out in September–December 2023 at the biodiversity study center at Bengkulu University. Observation results identified male C. amboinensis turtles with larger heads and brighter chins than female turtles. The carapace is oval with small bumps on vertebral 5 and wider marginal edges than in female turtles; the male's plastron displays a distinctive concave while the females have a flatter plastron. Male turtles have longer and thicker tails than female turtles. There are differences in the morphological characteristics of male and female C. amboinensis turtles, specifically in the head, carapace, plastron, and tail morphology.

Distribution and reference values of peripheral perfusion index in neonates from population-wide screening

BackgroundPeripheral perfusion index (PPI) is useful in a variety of neonatal settings. Currently, available reference values are from small numbers and highly variable.MethodsWe sought to generate reference values of PPI...

Negative Binomial Three Parameter Lindley Distribution and Its Properties

Many researchers have proposed mixed distributions as one of the most important methods for obtaining new probability distributions. Several studies have shown that mixed Negative Binomial distributions fits count data better than Poisson and Negative Binomial distribution itself. In this paper, we introduce a mixed distribution by mixing the distributions of negative binomial and three Parameter Lindley distribution. This new distribution has a thick tail and may be considered as an alternative for fitting count data with over dispersion. The parameters of the new distribution are estimated using MLE method and properties studied. Special cases of the new distribution and also identified. A simulation study carried out shows that the ML estimators give the parameter estimates close to the parameter when the sample is large, that is, the bias and variance of the parameter estimates decrease with increase in sample size showing the consistent nature of the new compound distribution. The study also compares the performance of the new distribution over distributions of Poisson, Negative Binomial, Negative Binomial oneParameter Lindley Distribution, Negative Binomial two Parameter distribution, three parameter Lindley distribution using a real count over dispersed dataset and the results shows that Negative Binomial three parameter Lindley distribution gave the smallest Kolmogorov Smirnov test statistic, AIC and BIC as compared to other distributions, hence the new distribution provided a better fit compared to other distributions under study for fitting over dispersed count data.

The climate niche of Homo Sapiens

The increasing atmospheric concentrations of greenhouse gases will place humans in climates that are unprecedented in the evolution of the species. I use the ecological definition of the human niche in climate space, and combine this with a new constellation of methods from extreme value statistics to study human occupation near the boundaries of that niche. I find that the temperature distribution has a thin tail whereas the tail of precipitation is thick. This thick tail reflects that humans are used to a wide range of rainfall regimes, so future precipitation changes, although leading to unprecedented rainfall, are less likely to pose a major challenge. An increase in temperature, on the other hand, will put hundreds of millions of people in heat that is not just unprecedented and but also hard to imagine from extrapolating current temperatures. These findings are qualitatively similar but an order of magnitude smaller than previous studies.

Interval evaluation of wind power prediction based on skew-slash t distribution

Wind resources have characteristics of stochastic volatility, resulting in wind power forecast errors greatly. The short and medium-term wind power forecast error distribution of the actual wind farm operating system is analyzed, and a sharp peak and thick tail, with heavy tail and skewness characteristics, are presented. A skew-slash t distribution (SST distribution) is proposed to describe the error distribution of short-term wind power prediction, and the parameter estimation is carried out by probability density curve fitting. The fitting results of the wind power forecast error historical data of the Wind power plant based on SST distribution, t distribution, and t Location-slash distribution (TLS distribution) are obtained, and the fitting goodness and prediction accuracy are compared. The results show that the SST distribution can more effectively estimate the wind power prediction interval.

Comparative skeletal anatomy of salt marsh and western harvest mice in relation to locomotor ecology.

The salt marsh harvest mouse (Reithrodontomys raviventris) is an endangered species, endemic to the San Francisco Bay Estuary, that co-occurs with the more broadly distributed species, the western harvest mouse (Reithrodontomys megalotis). Despite their considerable external morphological similarities, the northern subspecies of salt marsh harvest mice have relatively longer and thicker tails than do western harvest mice, which may be related to their abilities to climb emergent marsh vegetation to avoid tidal inundation. We used micro-CT to compare post-cranial skeletal anatomy between the salt marsh and western harvest mouse, to examine whether the salt marsh harvest mouse's restriction to brackish marshes is associated with skeletal adaptations for scansorial locomotion. We found that salt marsh harvest mice exhibited a deeper 3rd caudal vertebra, a more caudally located longest tail vertebra, craniocaudally longer tail vertebrae, and a longer digit III proximal phalanx than western harvest mice. These phalangeal and vertebral characteristics are known to decrease body rotations during climbing, increase contact with substrates, and decrease fall susceptibility in arboreal mammals, suggesting that the salt marsh harvest mouse may be morphologically specialized for scansorial locomotion, adaptive for its dynamic wetland environment.

The changes in the annual distribution of mountain runoff during the period of 1965–2018 in Hexi Corridor, Northwest China

The annual distribution characteristics of river runoff in arid regions have significant implications for water resource stability and management. Based on the mountain runoff data from 1965 to 2018, this study examines the annual change characteristics of monthly runoff of the Shiyang River Basin, Heihe River Basin, and Shule River Basin in the Hexi Corridor, Northwest China. Many indexes are used and analyzed, including the coefficient of variance, the complete regulation coefficient, the concentration degree and concentration period, the magnitude of change, the skewness coefficient, and the kurtosis coefficient of the annual distribution curves. The results reveal the following: (1) The inhomogeneity of annual runoff distribution in the Taolai River and the rivers to the west of it, except the Shiyou River, show an increasing trend. Conversely, the inhomogeneity of the rivers to the east of the Taolai River generally show a downward trend, but the coefficient of variance value is still very high. (2) In the Shiyang River Basin, the annual distribution of the concentration period is characterized by a relatively discrete pattern. Conversely, the Heihe River Basin exhibits a relatively concentrated pattern, and the distribution pattern of the Shule River Basin is quite different. Notably, all concentration periods in the three basins have shifted backward after the 2000s. (3) The Shiyang River Basin exhibits disordered annual distribution curves of runoff in different years. In contrast, the Heihe River Basin presents a typical ‘single-peak’ pattern with a prominent right-skewed. The Shule River Basin has regular distribution curves, with a gradually significant ‘double-peak’ pattern from east to west. Overall, there has been a slight change in runoff in the Shiyang River Basin, while the Heihe River Basin and Shule River Basin have experienced significant increases in runoff. The annual distribution curves of runoff in the Liyuan River and the rivers to the east of it exhibit a gentle peak pattern, and the appearance probability of extreme runoff during the year is low. Conversely, the rivers to the west of the Liyuan River, excluding the Danghe River, display a sharp peak and thick tail pattern, indicating that the appearance probability of extreme runoff during the year is high. These findings have practical implications for the planning and management of water resources in the Hexi Corridor. Moreover, they provide a solid foundation for predicting future changes in regional water resources.

Exploring skill distribution tails through stochastic dominance

SummaryLocation choices of differently skilled workers are analyzed in previous work on labor mobility, which proposes a model that suggests thicker tails in the skill distributions of large cities. This paper replicates the empirical findings of this work by using quantile regression and density plots as employed in the existing study, while also suggesting an alternative testing method for thick tails in the form of an initial stochastic dominance test. The test reveals clear evidence of a thicker lower tail, but the results are less clear for the upper tail, which raises some questions on how to best handle extreme upper tails of skill distributions.

Shanghai Crude Oil Futures Yield Volatility Study

Since the listing of Shanghai crude oil futures in March 2018 its market performance has gradually attracted attention. The closing price data of the futures for the period from March 26, 2018 to April 17, 2023 are selected as observations, and a GARCH model is fitted to the futures log return series to analyze the development of Shanghai crude oil futures and its future trend. The study finds that extreme events such as the New Crown epidemic and the Russia-Ukraine conflict had led to high volatility of Shanghai crude oil futures, but the volatility gradually stabilized in the context of the double cycle at home and abroad. The study compares the effectiveness of the GARCH(1,1)-T model and the GARCH(1,1)-GED model in fitting the logarithmic returns of the Shanghai crude oil futures market. the GARCH(1,1)-T model is able to better capture the asymmetry of the market volatility and the phenomenon of sharp peaks and thick tails after taking into account the distributional characteristics of the residuals. In the paper, the closing price of Shanghai crude oil futures in the next 10 days is predicted according to the GARCH(1,1)-T model, and the short-term prediction effect is better.

Identification-robust methods for comparing inequality with an application to regional disparities

We propose Fieller-type methods for inference on generalized entropy inequality indices in the context of the two-sample problem which covers testing the statistical significance of the difference in indices, and the construction of a confidence set for this difference. In addition to irregularities arising from thick distributional tails, standard inference procedures are prone to identification problems because of the ratio transformation that defines the considered indices. Simulation results show that our proposed method outperforms existing counterparts including simulation-based permutation methods and results are robust to different assumptions about the shape of the null distributions. Improvements are most notable for indices that put more weight on the right tail of the distribution and for sample sizes that match macroeconomic type inequality analysis. While irregularities arising from the right tail have long been documented, we find that left tail irregularities are equally important in explaining the failure of standard inference methods. We apply our proposed method to analyze income per-capita inequality across U.S. states and non-OECD countries. Empirical results illustrate how Fieller-based confidence sets can: (i) differ consequentially from available ones leading to conflicts in test decisions, and (ii) reveal prohibitive estimation uncertainty in the form of unbounded outcomes which serve as proper warning against flawed interpretations of statistical tests.

Navigating Market Turbulence: Exploring Banking Sector Volatility Amidst COVID-19

The objective of the study was to study the volatility in the banking industry during COVID-19 by employing the technical barometer Relative Strength Index. The secondary data was extracted from the official websites of the National Stock Exchange for the period 1st January, 2020 to 30th September, 2022. The top 5 banks of Bank Nifty Index were undertaken for the analysis purpose and it was found that the maximum average return was witnessed by SBI Bank during the period of study. The returns of HDFC Bank, AXIS Bank, SBI Bank and Kotak Bank were fairly symmetrical as their values lies between -0.5 and 0.5. The returns of ICICI bank were moderately skewed as the value is -0.78. The high values of the excess kurtosis indicates that returns are heavily peaked and possesses thick tails as the values among all banks is greater than 1. The median return is highest in case of ICICI Bank and lowest in case of HDFC Bank. It was further witnessed that in the year 2020, due to COVID-19, the stock prices declined measurably and entered the oversold zone with RSI value of 18.98 on 24th March, 2020. Thereafter, there were continuous ups and downs in stock prices due to panic and unrest during the pandemic phase. The chart of Bank Nifty index was normal and there were many occasions when it appeared bullish and bearish to investors. Due to the change in behaviour of the individual investors there was panic buying and selling in the market.

Transition E-Garch Model for Modeling and Forecasting Volatility of Equity Stock Returns in Nigeria Stock Exchange

The mean-equations that exhibit unconditional variance do not reflect real-world data characteristics and do not always fully embrace the thick tail properties of high-frequency financial time series. However, there are cases when mean-equations exhibit conditional and unconditional variances, which conventional Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models do not accommodate with assumptions of normal error innovation. The behaviour of equity in stock returns volatility was investigated using mean-equations that reflect both conditional and unconditional variances under the variants innovation distribution. The Nigeria Stock Exchange’s, (NSE’s), daily All Stock Index, (ASI) data from 3rd May 1999 to 18th March 2019 was utilized to characterize the volatility structure of equity in Nigeria Stock returns. The Transition Exponential GARCH Model (TEGM) with non-normal innovations was used to demonstrate the dynamic model performance and predictive power in modeling variances that transit between unconditional and conditional structures. Under various error innovations, the structural characteristics of the TEGM were examined, and the parameters were estimated. The TEGM result under Student’s t innovation distribution was significant for forecasting and predicting random series data. The error distribution has both the minimal and sufficient requirements for the best predictive capacity and forecasting capabilities. Over a longer period, the NSE’s daily ASI showed more unconditional variance than conditional variation. The Transition Exponential GARCH Model was found to be the best model for describing the volatility structure of financial assets in Nigerian stock returns, and is thus recommended for making informed investment decisions with better forecast performance.

Antimicrobial growth promoters approved in food-producing animals in South Africa induce shiga toxin-converting bacteriophages from Escherichia coli O157:H7.

In this study, four antimicrobial growth promoters, including virginiamycin, josamycin, flavophospholipol, poly 2-propenal 2-propenoic acid and ultraviolet light, were tested for their capacity to induce stx-bacteriophages in 47 Shiga toxin-producing E. coli O157:H7 isolates. Induced bacteriophages were characterized for shiga toxin subtypes and structural genes by PCR, DNA restriction fragment length polymorphisms (RFLP) and morphological features by electron microscopy. Bacteriophages were induced from 72.3% (34/47) of the STEC O157:H7 isolates tested. Bacteriophage induction rates per induction method were as follows: ultraviolet light, 53.2% (25/47); poly 2-propenal 2-propenoic acid, 42.6% (20/47); virginiamycin, 34.0% (16/47); josamycin, 34.0% (16/47); and flavophospholipol, 29.8% (14/47). A total of 98 bacteriophages were isolated, but only 59 were digestible by NdeI, revealing 40 RFLP profiles which could be subdivided in 12 phylogenetic subgroups. Among the 98 bacteriophages, stx2a, stx2c and stx2d were present in 85.7%, 94.9% and 36.7% of bacteriophages, respectively. The Q, P, CIII, N1, N2 and IS1203 genes were found in 96.9%, 82.7%, 69.4%, 40.8%, 60.2% and 73.5% of the samples, respectively. Electron microscopy revealed four main representative morphologies which included three bacteriophages which all had long tails but different head morphologies: long hexagonal head, oval/oblong head and oval/circular head, and one bacteriophage with an icosahedral/hexagonal head with a short thick contractile tail. This study demonstrated that virginiamycin, josamycin, flavophospholipol and poly 2-propenal 2-propenoic acid induce genetically and morphologically diverse free stx-converting bacteriophages from STEC O157:H7. The possibility that these antimicrobial growth promoters may induce bacteriophages in vivo in animals and human hosts is a public health concern. Policies aimed at minimizing or banning the use of antimicrobial growth promoters should be promoted and implemented in countries where these compounds are still in use in animal agriculture.

An Extended Zeta Function with Applications in Model Building and Bayesian Analysis

In certain problems in model building and Bayesian analysis, the results end up in forms connected with generalized zeta functions. This necessitates the introduction of an extended form of the generalized zeta function. Such an extended form of the zeta function is introduced in this paper. In model building situations and in various types of applications in physical, biological and social sciences and engineering, a basic model taken is the Gaussian model in the univariate, multivariate and matrix-variate situations. A real scalar variable logistic model behaves like a Gaussian model but with a thicker tail. Hence, for many of industrial applications, a logistic model is preferred to a Gaussian model. When we study the properties of a logistic model in the multivariate and matrix-variate cases, in the real and complex domains, invariably the problem ends up in the extended zeta function defined in this paper. Several such extended logistic models are considered. It is also found that certain Bayesian considerations also end up in the extended zeta function introduced in this paper. Several such Bayesian models in the multivariate and matrix-variate cases in the real and complex domains are discussed. It is stated in a recent paper that “Quantum Mechanics is just the Bayesian theory generalized to the complex Hilbert space”. Hence, the models developed in this paper are expected to have applications in quantum mechanics, communication theory, physics, statistics and related areas.

Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets

The distributions for highly volatile financial time-series data are playing an increasingly important role in current financial scenarios and signal analyses. An important characteristic of such a probability distribution is its tail behaviour, determined through its tail thickness. This can be achieved by estimating the index parameter of the corresponding distribution. The normal and Cauchy distributions, and, sometimes, a mixture of the normal and Cauchy distributions, are suitable for modelling such financial data. The family of stable distributions can provide better modelling for such financial data sets. Financial data in high-volatility markets may be better modelled, in many cases, by the Linnik distribution in comparison to the stable distribution. This highly flexible family of distributions is better capable of modelling the inflection points and tail behaviour compared to the other existing models. The estimation of the tail thickness of heavy-tailed financial data is important in the context of modelling. However, the new probability distributions do not admit any closed analytical form of representation. Thus, novel methods need to be developed, as only a few can be found in the literature. Here, we recall a recent novel method, developed by the authors, based on a trigonometric moment estimator using circular distributions. The linear data may be transformed to yield circular data. This transformation is solely for yielding a suitable estimator. Our aim in this paper is to provide a review of the few existing methods, discuss some of their drawbacks, and also provide a universal (∀α∈(0,2]), efficient, and easily implementable estimator of α based on the transformation mentioned above. Novel, circular-statistics-based tests for the index parameter α of the stable and Linnik distributions are introduced and also exemplified with real-life financial data. Two real-life data sets are analysed to exemplify the methods recommended and enhanced by the authors.

Application of Asymmetric-GARCH Type Models to The Kenyan Exchange Rates

Modelling and forecasting the volatility of a financial time series has become essential in many economic and financial applications like portfolio optimization and risk management. The symmetric-GARCH type models can capture volatility and leptokurtosis. However, the models fail to capture leverage effects, volatility clustering, and the thick tail property of high-frequency financial time series. The main objective of this study was to apply the asymmetric-GARCH type models to Kenyan exchange to overcome the shortcomings of symmetric-GARCH type models. The study compared the asymmetric Conditional Heteroskedasticity class of models: EGARCH, TGARCH, APARCH, GJR-GARCH, and IGARCH. Secondary data on the exchange rate from January 1993 to June 2021 were obtained from the Central Bank of Kenya website. The best fit model is determined based on parsimony of the Akaike Information Criterion (AIC), Bayesian Information Criterion (BIC), Log-Likelihood criterion, and minimisation of prediction production errors (Mean error [ME] and Root Mean Absolute error [RMAE]). The optimal variance equation for the exchange rates data was APARCH (1,1) - ARMA (3,0) model with a skewed normal distribution (AIC = -4.6871, BIC = -4.5860). Volatility clustering was present in exchange rate data with evidence of the leverage effect. Estimated Kenya’s exchange rate volatility narrows over time, indicating sustained exchange rate stability.