Asymptotic Dependence Research Articles

Analytical Solutions for a Nonlinear Quadratic Delayed Functional Integral Inclusion With Feedback Control on the Real Half-Line

Let E be a reflexive Banach space. In this research, we are interested in the solvability of the nonlinear quadratic delayed functional integral inclusion (NQDFII) with a feedback control condition on the real half-axis. Our examination is found within the space BC(R+, E) of bounded continuous functions on the real half-axis R+ and takes values in a reflexive Banach space E beneath the assumption that the set-valued function G satisfy Lipschitz condition in E. The base we depend on in this study is the procedure related to a measure of noncompactness in the space BC(R+, E) by a given norm of continuity and applying Darbo’s fixed point theorem. Moreover, the asymptotic stability of the solution and the asymptotic dependency of the solution on the set of selections SG will be examined. Also, we give an example to illustrate the adequacy and esteem of our comes about.

Scalable Methods for Multiple Time Series Comparison in Second Order Dynamics

Statistical comparison of multiple time series in their underlying frequency patterns has many real applications. However, existing methods are only applicable to a small number of mutually independent time series, and empirical results for dependent time series are only limited to comparing two time series. We propose scalable methods based on a new algorithm that enables us to compare the spectral density of a large number of time series. The new algorithm helps us efficiently obtain all pairwise feature differences in frequency patterns between M time series, which plays an essential role in our methods. When all M time series are independent of each other, we derive the joint asymptotic distribution of their pairwise feature differences. The asymptotic dependence structure between the feature differences motivates our proposed test for multiple mutually independent time series. We then adapt this test to the case of multiple dependent time series by partially accounting for the underlying dependence structure. Additionally, we introduce a global test to further enhance the approach. To examine the finite sample performance of our proposed methods, we conduct simulation studies. The new approaches demonstrate the ability to compare a large number of time series, whether independent or dependent, while exhibiting competitive power. Finally, we apply our methods to compare multiple mechanical vibrational time series.

Improving estimation for asymptotically independent bivariate extremes via global estimators for the angular dependence function

Modelling the extremal dependence of bivariate variables is important in a wide variety of practical applications, including environmental planning, catastrophe modelling and hydrology. The majority of these approaches are based on the framework of bivariate regular variation, and a wide range of literature is available for estimating the dependence structure in this setting. However, such procedures are only applicable to variables exhibiting asymptotic dependence, even though asymptotic independence is often observed in practice. In this paper, we consider the so-called ‘angular dependence function’; this quantity summarises the extremal dependence structure for asymptotically independent variables. Until recently, only pointwise estimators of the angular dependence function have been available. We introduce a range of global estimators and compare them to another recently introduced technique for global estimation through a systematic simulation study, and a case study on river flow data from the north of England, UK.

Asymptotic Dependence and Its Impact on Hedging Effectiveness: An Examination of Stock, Currency, and Commodity Futures

ABSTRACTThis study measures the asymptotic dependence between spot and futures losses and investigates its impact on hedging effectiveness using data from stock, currency, and commodity markets. The findings reveal that stock futures contracts show strong asymptotic dependence, while currency futures have weak asymptotic dependence and most commodity futures lack asymptotic dependence with the underlying spots. Further, stock futures have the highest hedging effectiveness, while commodity and currency futures show low hedging effectiveness for downside risk. Results also suggest that asymptotic dependence is critical for minimum‐variance hedging. Asymptotic dependence increases with the hedging horizon, leading to a better hedging performance of the futures. It also appears that the hedging strategies sensitive to asymptotic dependence perform better than the competing models. The results for the entire period and the subsample periods offer similar conclusions.

Portfolio default losses driven by idiosyncratic risks

We consider a portfolio of general defaultable assets with low individual default risk and study the probability of the portfolio default loss exceeding an arbitrary threshold. The latent variables driving defaults are modeled by a mixture structure that combines common shock, systematic risk, and idiosyncratic risk factors. While common shocks and systematic risk have been found by many studies to contribute significantly to portfolio losses, the role of idiosyncratic risks is often found to be negligible. Such conclusions are usually established under the assumption that the portfolio size tends to infinity and idiosyncratic risk factors are not dominant. We study under-investigated scenarios where the portfolio size is fixed and the idiosyncratic risk factors are heavy-tailed, exploring two distinct scenarios: an independence scenario and an asymptotic dependence scenario. The former is standard in the literature, while the latter is motivated by recent studies that have found the inadequacy of relying solely on common factors to capture default clustering. This consideration also reflects the possibility that idiosyncratic reasons can trigger contagion among firms with liabilities to each other. In the independence scenario, even with heavy-tailed idiosyncratic risk factors, the probability of a substantial portfolio loss remains low unless a single asset carries a disproportionately large weight. Conversely, in the asymptotic dependence scenario, the primary drivers of increased exceedance probability are the dependent idiosyncratic risk factors.

Multi-Stage Mathematical Programming Models and Their Applications in Agriculture

The article presents multi-stage parametric programming models, the characteristics of which depend on time and seasonality. The first model took into account the impact on the yield of agricultural crops of predecessors. In the second model, related to the distribution of sales of products by seasons, at the first stage, a point and interval forecast of the task parameters is carried out, at the second stage, optimal coefficients are determined that characterize the volume of sales of crop products depending on the season. Then, based on the obtained forecasts and optimal coefficients, the parametric programming problem is solved. The described tasks are implemented on real objects of the Irkutsk region. Logistic and asymptotic dependences are used to predict crop yields, and the price trend is a seasonal model. It should be noted that the presented models can be refined with the help of expert assessments, which will improve the adequacy of planning the activities of agricultural producers.

Asymptotics for ruin probabilities in a bidimensional discrete-time risk model with dependent and consistently varying tailed net losses

Consider an insurer who operates two lines of businesses and hence receives two types of insurance net losses. In the bidimensional discrete-time risk model with a constant interest rate, the net loss vectors from the two business lines form a sequence of independent and identically distributed real-valued random vectors. We propose a bidimensional extended regularly varying structure in terms of survival copulas to model the dependence between the two components of each net loss vector, which includes not only asymptotic independence but also asymptotic dependence. Under the framework of consistent variation, we obtain several (uniformly) asymptotic formulas for various ruin probabilities. In particular, the investigation of random-time ruin probabilities unifies and extends the results on both finite-time and infinite-time ruin probabilities. Some numerical studies are also performed to check the accuracy of our obtained asymptotic results.

Bayesian smoothing for time-varying extremal dependence

Abstract We propose a Bayesian time-varying model that learns about the dynamics governing joint extreme values over time. Our model relies on dual measures of time-varying extremal dependence, that are modelled via a suitable class of generalized linear models conditional on a large threshold. The simulation study indicates that the proposed methods perform well in a variety of scenarios. The application of the proposed methods to some of the world’s most important stock markets reveals complex patterns of extremal dependence over the last 30 years, including passages from asymptotic dependence to asymptotic independence.

An Investigation of a Nonlinear Delay Functional Equation with a Quadratic Functional Integral Constraint

This research paper focuses on investigating the solvability of a constrained problem involving a nonlinear delay functional equation subject to a quadratic functional integral constraint, in two significant cases: firstly, the existence of nondecreasing solutions in a bounded interval L1[0,T] and, secondly, the existence of nonincreasing solutions in unbounded interval L1(R+). Moreover, the paper explores various qualitative properties associated with these solutions for the given problem. To establish the validity of our claims, we employ the De Blasi measure of noncompactness (MNC) technique as a basic tool for our proofs. In the first case, we provide sufficient conditions for the uniqueness of the solution ψ∈L1[0,T] and rigorously demonstrate its continuous dependence on some parameters. Additionally, we establish the equivalence between the constrained problem and an implicit hybrid functional integral equation (IHFIE). Furthermore, we delve into the study of Hyers–Ulam stability. In the second case, we examine both the asymptotic stability and continuous dependence of the solution ψ∈L1(R+) on some parameters. Finally, some examples are provided to verify our investigation.

Asymptotic Stability and Dependency of a Class of Hybrid Functional Integral Equations

Here, we discuss the solvability of a class of hybrid functional integral equations by applying Darbo’s fixed point theorem and the technique of the measure of noncompactness (MNC). This study has been located in space BC (R+). Furthermore, we prove the asymptotic stability of the solution of our problem on R+. We introduce the idea of asymptotic dependency of the solutions on some parameters for that class. Moreover, general discussion, examples, and remarks are demonstrated.

Statistical modelling of dependence between net demands and deficits in two area power systems

Power system resource adequacy risks is dominated by the extremes of the relevant distributions or processes: the upper tail of demand and the lower tail of available generation. Because of this, relevant data in the historic record are sparse. Moreover, for interconnected systems, the degree of statistical dependence in these extremes between systems can also have a sizeable impact on the level of risk in each system. This paper uses results from statistical extreme value theory (EVT) to fit smoothed joint distributions for the values of (demand minus available renewables) and of surplus/deficit dependence in a two-area system, using data from the Irish and Great Britain power system for examples.As well as the statistical smoothing mitigating the consequences of limited volumes of data, the concept of asymptotic dependence provides a useful explanation of the strength of dependence. There is strong evidence that the deficits in the GB and Ireland systems are asymptotically independent, whereas there is evidence for asymptotic dependence in the distributions of (demand minus available wind capacity). This is consistent with the intuition that, when independent distributions of conventional capacity are convoluted with those of demand and wind, the dependence is weakened. The consequent use of a Gaussian copula to describe the dependence of deficits provides a convenient means of carrying out sensitivity analysis to the strength of relationship.

Speed-up of traveling waves by negative chemotaxis

We consider the traveling wave speed for Fisher-KPP (FKPP) fronts under the influence of repulsive chemotaxis and provide an almost complete picture of its asymptotic dependence on parameters representing the strength and length-scale of chemotaxis. Our study is based on establishing the convergence to the porous medium FKPP traveling wave and a hyperbolic FKPP-Keller-Segel traveling wave in certain asymptotic regimes. In this way, it clarifies the relationship between three equations that have each garnered intense interest on their own. Our proofs involve a variety of techniques ranging from entropy methods and decay of oscillations estimates to a general description of the qualitative behavior to the hyperbolic FKPP-Keller-Segel equation. For this latter equation, we, as a part of our limiting arguments, establish a new explicit lower bound on the minimal traveling wave speed and provide a novel construction of traveling waves that extends the known existence range to all parameter values.

Large population limit of the spectrum of killed birth-and-death processes

We consider a general class of birth-and-death processes with state space {0,1,2,3,…} which describes the size of a population going eventually to extinction with probability one. We obtain the complete spectrum of the generator of the process killed at 0 in the large population limit, that is, we scale the process by a parameter K, and take the limit K→+∞. We assume that the differential equation dx/dt=b(x)−d(x) describing the infinite population limit (in any finite-time interval) has a repulsive fixed point at 0, and an attractive fixed point x⁎>0. We prove that, asymptotically, the spectrum is the superposition of two spectra. One is the spectrum of the generator of an Ornstein-Uhlenbeck process, which is n(b′(x⁎)−d′(x⁎)), n≥0. The other one is the spectrum of a continuous-time binary branching process conditioned on non-extinction, and is given by n(d′(0)−b′(0)), n≥1. A major difficulty is that different scales and function spaces are involved. We work at the level of the eigenfunctions that we split over different regions, and study their asymptotic dependence on K in each region. In particular, we prove that the spectral gap goes to min⁡{b′(0)−d′(0),d′(x⁎)−b′(x⁎)}. This work complements a previous work of ours in which we studied the approximation of the quasi-stationary distribution and of the mean time to extinction.

Optimal Amplitude–Density Synthesis of Linear Aperiodic Arrays

New deterministic procedures for the design of linear aperiodic arrays are described which permit exploiting, in a combined way, both the positions and the excitation amplitudes of the array elements obtaining a pattern which optimally fits, in terms of a weighted L2 norm, the pattern of a reference linear continuous aperture. A first numerical procedure is based on alternating optimization of positions and amplitudes by means of closed-form convex projectors. Sufficient conditions for the solution to be optimal are established. A second numerical procedure is based on a domino-like sequential determination of the unknowns which can be iterated to convergence. Additionally, analytical asymptotic expressions for the optimal inter-element spacing and amplitude are derived by means of variational techniques. The optimal asymptotic inter-element spacing is demonstrated to be proportional to the reference tapering to the power (-2/3) while the optimal asymptotic array amplitude is proportional to the reference tapering to the power (1/3). For aperiodic arrays with equiamplitude excitation it is proved that the optimal inter-element spacing is proportional to the reference tapering to the power (-1). Based on these asymptotic dependencies, closed-form analytical solutions are obtained for amplitudes and positions of the elements. Several numerical results confirm the effectiveness and accuracy of the new procedures.

Logarithmic corrections to O(a) and O(a^2) effects in lattice QCD with Wilson or Ginsparg–Wilson quarks

We derive the asymptotic lattice spacing dependence a^n[2b_0bar{g}^2(1/a)]^{hat{Gamma }_i} relevant for spectral quantities of lattice QCD, when using Wilson, textrm{O}(a) improved Wilson or Ginsparg–Wilson quarks. We give some examples for the spectra encountered for hat{Gamma }_i including the partially quenched case, mixed actions and using two different discretisations for dynamical quarks. This also includes maximally twisted mass QCD relying on automatic textrm{O}(a) improvement. At textrm{O}(a^2), all cases considered have min _ihat{Gamma }_igtrsim -0.3 if N_{textrm{f}}le 4, which ensures that the leading order lattice artifacts are not severely logarithmically enhanced in contrast to the O(3) non-linear sigma model (Balog et al. in Nucl Phys B 824:563–615, 2010; Balog et al. in Phys Lett B 676:188–192, 2009). However, we find a very dense spectrum of these leading powers, which may result in major pile-ups and cancellations. We present in detail the computational strategy employed to obtain the 1-loop anomalous dimensions already used in Husung et al. (Phys Lett B 829:137069, 2022).

A random parameters copula-based binary logit-generalized ordered logit model with parameterized dependency: Application to active traveler injury severity analysis

A copula-based dependence approach accommodates various facets of dependence structures in building multivariate stochastic models. In existing studies, applications of copula for ordinal random variables are predominantly modeled by employing traditional ordered models (ordered logit/probit) while assuming the effects of parameters to remain the same across all observations. The methodological contributions of this study are grounded in addressing the abovementioned significant methodological gaps in the application of copula formulation by proposing a copula-based random parameters nominal-ordinal joint model construct of correlated random variables. Specifically, we propose and develop a random parameters binary logit-generalized ordered logit copula formulation while also complementing the proposed approach by accommodating the effects of unobserved heterogeneity in parameter estimates. To the best of the authors’ knowledge, this study is the first instance to incorporate generalized ordered formulation within copula in extant econometrics literature. Further, to obtain a direct effect of exogenous variables on dependence, we parameterize the copula dependence structure as a function of different covariates in six different copula structures including a wide range of dependency structures which represent radial symmetry and asymmetry, and asymptotic tail dependence. The empirical contributions of this study are grounded in the application of the proposed copula-based formulation by examining ‘active traveler (pedestrian and bicyclist) crash type’ and ‘active traveler injury severity outcomes’ as two dimensions of active travel injury severity mechanism. The model is estimated by using crash data for the years 2012 through 2018 from the state of Queensland, Australia, by employing a comprehensive set of exogenous variables. In addition, the analyses are further augmented by complementing the elasticity effects of exogenous variables.

Asymptotic shape of the concave majorant of a Lévy process

We establish distributional limit theorems for the shape statistics of a concave majorant (i.e. the fluctuations of its length, its supremum, the time it is attained and its value at $T$) of any Levy process on $[0,T]$ as $T\to\infty$. The scale of the fluctuations of the length and other statistics, as well as their asymptotic dependence, vary significantly with the tail behaviour of the Levy measure. The key tool in the proofs is the recent representation of the concave majorant for all Levy processes using a stick-breaking representation.

Asymmetric tail dependence modeling, with application to cryptocurrency market data

Since the inception of Bitcoin in 2008, cryptocurrencies have played an increasing role in the world of e-commerce, but the recent turbulence in the cryptocurrency market in 2018 has raised some concerns about their stability and associated risks. For investors it is crucial to uncover the dependence relationships between cryptocurrencies for a more resilient portfolio diversification. Moreover, the stochastic behavior in both tails is important, as long positions are sensitive to a decrease in prices (lower tail), while short positions are sensitive to an increase in prices (upper tail). In order to assess both risk types, we develop in this paper a flexible copula model which is able to distinctively capture asymptotic dependence or independence in its lower and upper tails simultaneously. Our proposed model is parsimonious and smoothly bridges (in each tail) both extremal dependence classes in the interior of the parameter space. Inference is performed using a full or censored likelihood approach, and we investigate by simulation the estimators’ efficiency under three different censoring schemes which reduce the impact of nonextreme observations. We also develop a local likelihood approach to capture the temporal dynamics of extremal dependence among pairs of leading cryptocurrencies. We here apply our model to historical closing prices of five leading cryotocurrencies which share large cryptocurrency market capitalizations. The results show that our proposed copula model outperforms alternative copula models and that the lower-tail dependence level between most pairs of leading cryptocurrencies and, in particular, Bitcoin and Ethereum has become stronger over time, smoothly transitioning from an asymptotic independence regime to an asymptotic dependence regime in recent years, whilst the upper tail has been relatively more stable overall at a weaker dependence level.

Asymptotic analysis of a dynamic systemic risk measure in a renewal risk model

In the context of insurance, we propose a dynamic systemic risk measure based on a multi-dimensional renewal risk model to describe the instant expected shortfall of an insurer at the moment when one of its business lines suffers crisis (i.e., deficit). The asymptotic behavior of the measure is studied in both the asymptotic independence and asymptotic dependence cases, and some asymptotic formulas with the uniformity in the whole time horizon are derived when the claim size distributions belong to the class of regular variation. The obtained results do not depend on specific setups of the renewal claim-number process, and they are also insensitive to specific dependence structures in the asymptotic independence case. These facts make our results concise in form and flexible in application. More interestingly, our results for the corresponding discounted version of the measure have nothing to do with the time variable. Hence, the discounted version of the measure can be regarded approximately as a static (i.e., time-invariant) risk measure of the dynamic system.

A model for space-time threshold exceedances with an application to extreme rainfall

In extreme value studies, models for observations exceeding a fixed high threshold have the advantage of exploiting the available extremal information while avoiding bias from low values. In the context of space-time data, the challenge is to develop models for threshold exceedances that account for both spatial and temporal dependence. We address this issue through a modelling approach that embeds spatial dependence within a time series formulation. The model allows for different forms of limiting dependence in the spatial and temporal domains as the threshold level increases. In particular, temporal asymptotic independence is assumed, as this is often supported by empirical evidence, especially in environmental applications, while both asymptotic dependence and asymptotic independence are considered for the spatial domain. Inference from the observed exceedances is carried out through a combination of pairwise likelihood and a censoring mechanism. For those model specifications for which direct maximization of the censored pairwise likelihood is unfeasible, we propose an indirect inference procedure which leads to satisfactory results in a simulation study. The approach is applied to a dataset of rainfall amounts recorded over a set of weather stations in the North Brabant province of the Netherlands. The application shows that the range of extremal patterns that the model can cover is wide and that it has a competitive performance with respect to an alternative existing model for space-time threshold exceedances.