Parameter Restrictions Research Articles

Analysis of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes

In this paper, we investigate the dynamics of a stochastic predator–prey system with modified Leslie–Gower and Holling-type IV schemes. We first show the existence and uniqueness of the global positive solution to the system with positive initial values. In some case, the stochastic boundedness and stochastic permanence are obtained. Then, under some conditions, we prove the persistence in mean and extinction of the stochastic system. Moreover, under certain parametric restrictions, we obtain that the system has a stationary distribution which is ergodic. Finally, some numerical simulations are carried out to support our results.

“Global factors, international spillovers, and the term structure of interest rates: New evidence for Asian Countries”

This paper provides new evidence about the role of common global factors exploring the existence of structural breaks in the long-run trend of the term structure and analyzes the spillover effects from the unconventional monetary policies recently implemented by major industrialized countries. For a panel of four Asian economies (Malaysia, Philippines, Singapore, South Korea), we show that, accounting for the role of global liquidity factors, parameters restrictions associated with the EHTS are not rejected, even after a regime-shift occurring at the end of 2005, thus supporting an extended weak version of the “Liquidity Premium Theory”. We also document relevant discrepancies in the short-run dynamics of long-term interest rates, which are strictly related to some structural differences between these Asian countries in terms of the “impossible trinity” between monetary independence, financial openness and exchange rate stability.

Constrained univariate and bivariate rational fractal interpolation

We study constrained natures of a new class of univariate and bivariate rational cubic fractal interpolation functions (RCFIFs). We derive the convergence results of the RCFIF towards an original function in In particular, when data lies (i) between two piecewise defined lines (ii) within a rectangle, we derive sufficient condition based on the restrictions of IFS parameters at fewer discretized values so that the corresponding RCFIF preserves the inherent property associated with constrained data. Using transfinite interpolation via blending functions, we extend constrained aspects to rational bivariate RCFIFs that lie above a piecewise plane and within a cuboid.

Analytical solitons with the Biswas-Milovic equation in the presence of spatio-temporal dispersion in non-Kerr law media

In this paper, we concentrate on the optical soliton solutions of spatially temporal Biswas-Milovic equation with power law and dual-power law nonlinearities. This model accounts for several imperfections for the transmission of solitons through optical fibers. The first integral method is employed in order to construct singular and dark 1-soliton solutions from the governing Biswas-Milovic equation with spatio-temporal dispersion. Some parametric restrictions are also enumerated which guarantee the existence of these soliton solutions. Moreover, the obtained results are demonstrated by 3D and 2D plots.

Valid corollaries of polarization-separated color attributes for a multi-layer dielectric structure

Herein, four corollaries for polarization-separated color attributes have been firstly proposed and experimentally verified based on the systematical investigations of a multi-layer dielectric structure L/(Ge/ZnS)3 (L stands for surface ZnS). Specifically, for different spectra responses to surface thicknesses dL (30, 60 and 90 nm) and incident angles θ (45°, 60° and 75°), color attributes of synthesis, s-polarization (s) and p-polarization (p) are systematically induced as: arithmetical averaging properties of luminance factors Ysynthesis% = (Ys% + Yp%)/2 or tristimulus values (Tv) Tv-synthesis = (Tv-s + Tv-p)/2; collinearity of synthetic and polarization-separated chromaticity coordinates (CCs); constant mathematic relation of Tv(s) > Tv(p); synthetic CCs partial to s-polarized CCs as dp-synthesis > ds-synthesis. These corollaries can be further generalized to common dielectric multi-layer structures due to the general derivation without any restrictions of the intrinsic parameters.

GMM Quantile Regresson

This paper develops generalized method of moments (GMM) estimation and inference procedures for quantile regression models. We propose a GMM estimator for simultaneous estimation across multiple quantiles. This estimator allows us to model quantile regression coefficients using flexible parametric restrictions across quantiles. The restrictions and simultaneous estimation lead to efficiency gains compared to standard methods. We establish the asymptotic properties of the GMM estimators when the number of quantiles used is fixed, and also when it diverges to infinity jointly with the sample size. As an alternative to GMM, we also propose a minimum distance (MD) estimator over a given subset of quantiles. We also provide specification tests for the imposed restrictions. The estimators and tests we propose are simple to implement in practice. Monte Carlo simulations provide numerical evidence of the finite sample properties of the methods. Finally, we apply the proposed methods to estimate the effects of smoking on birthweight of live infants at the extreme bottom of the conditional distribution.

Steady flow of one uniformly rotating fluid layer above another immiscible uniformly rotating fluid layer

The steady laminar flow of two immiscible, uniformly rotating fluid layers is studied and exact similarity solutions of the axisymmetric Navier-Stokes equations in cylindrical polar coordinates are found. The similarity solutions occur with a flat interface at z = 0 under the parameter restriction that σ²ρ = 1 where σ is the ratio of the fluid angular velocities at z = ±∞ and ρ is the density ratio of the two fluids. Under this restriction the problem reduces to one with two independent parameters, σ and μ, which is the viscosity ratio of the fluids. Numerical results of the resulting system of ODEs are found for selected values of μ and σ, and it is shown that similarity solutions exist for σc(μ)≤ σ ≤ 1 where σc(μ) ˂ 0 (i.e. counter-rotating flows). For σ ˂ 0 the lower fluid can become divided into two distinct recirculation regions between which fluid cannot transfer.

Cross Entropy Profiling to Test Pattern Synchrony in Short-Term Signals.

Examining nonlinear bi-variate time series for pattern synchrony has been largely carried out by the cross sample entropy measure, X-SampEn, which is highly bound by parametric restrictions. Threshold parameter r is the one that limits X-SampEn estimations most adversely. An inappropriate r choice leads to erroneous synchrony detection, even for the case of X-SampEn analysis on simple synthetically generated signals like the MIX(P) process. This gives us an intimation of how difficult it would be for such synchrony measures to handle the more complex physiologic data. The recently introduced concept of entropy profiling has been proved to release such measures from the clutches of r dependence. In this study, we demonstrate how entropy profiling with respect to r can be implemented on cross entropy analysis, particularly X-SampEn. We have used different sets of simple MIX(P) processes for the purpose and validated the impact of X-SampEn profiling over X-SampEn estimation, with a special focus on short-term data. From results, we see that X-SampEn profiling alone can accurately classify MIX(P) signals based on pattern synchrony. Here, X-SampEn estimation fails undoubtedly, even at the higher data lengths where traditional SampEn estimation is known to perform with good accuracy.

The Four Equation New Keynesian Model

This paper develops a New Keynesian model featuring financial intermediation, short- and long-term bonds, credit shocks, and scope for unconventional monetary policy. The log-linearized model reduces to four key equations -- a Phillips curve, an IS equation, and policy rules for the short-term nominal interest rate and the central bank's long bond portfolio (QE). The four equation model collapses to the standard three equation New Keynesian model under a simple parameter restriction. Credit shocks and QE appear in both the IS and Phillips curves. In equilibrium, optimal monetary policy entails adjusting the short-term interest rate to offset natural rate shocks, but using QE to offset credit market disruptions. Such policies can be supported by implementable rules in which the short-term interest rate reacts strongly to inflation and the central bank's bond portfolio reacts strongly to the output gap. The ability of the central bank to engage in QE significantly mitigates the costs of a binding zero lower bound.

Regression Discontinuity Designs Using Covariates

We study regression discontinuity designs when covariates are included in the estimation. We examine local polynomial estimators that include discrete or continuous covariates in an additive separable way, but without imposing any parametric restrictions on the underlying population regression functions. We recommend a covariate-adjustment approach that retains consistency under intuitive conditions and characterize the potential for estimation and inference improvements. We also present new covariate-adjusted mean-squared error expansions and robust bias-corrected inference procedures, with heteroskedasticity-consistent and cluster-robust standard errors. We provide an empirical illustration and an extensive simulation study. All methods are implemented in R and Stata software packages.

Revisiting advance disclosure of insider trading

We derive a parametric restriction necessary and sufficient for an equilibrium to exist in the model of Lenkey (2014). Given this restriction, the equilibrium is unique, correcting findings in the original article that multiple equilibria may exist with advance disclosure.

A Simple and Exact Simulation Approach to Heston Model

In this paper we will propose a simple approach to simulating Heston model efficiently and accurately. All existing simulation schemes so far directly work with the mean-reverting square root process of the variance in Heston model, instead we transform the variance to an equivalent volatility which follows a mean-reverting Ornstein-Uhlenbeck process. We will show it is more convenient to simulate the transformed volatility process than the original variance process since the new Ornstein-Uhlenbeck process does not have any term of square root, and is not restricted to any parameter restriction. Based on the transformed volatility process, we suggest a simple and exact scheme for the simulation of Heston model. Numerical examples show that the new scheme and Andersen's QE scheme perform very closely, and outperform other schemes such as log-normal scheme. While QE scheme suffers from the problem of leaking correlation, transformed volatility scheme does not, and therefore, provides a high-quality alternative to the existing simulation schemes for Heston model.

Optical soliton perturbation in parabolic law medium having weak non-local nonlinearity by a couple of strategic integration architectures

Abstract In this paper, the governing model with the inclusion of parabolic law nonlinearity, weakly non-local nonlinearity in addition to perturbation terms is examined for the sake of uncovering quite important optical soliton solutions. Dark, bright and singular solitons in addition to singular periodic solutions are yielded with the modified simple equation technique and trial equation architecture along with parameter restrictions.

Analysis of a stochastic predator-prey system with foraging arena scheme

ABSTRACTThis paper focuses on a predator-prey system with foraging arena scheme incorporating stochastic noises. This SDE model is generated from a deterministic framework by the stochastic parameter perturbation. We then study how the correlations of the environmental noises affect the long-time behaviours of the SDE model. Later on the existence of a stationary distribution is pointed out under certain parametric restrictions. Numerical simulations are carried out to substantiate the analytical results.

An IV framework for combining sign and long-run parametric restrictions in SVARs

This paper derives the sufficient conditions on the coefficients in a system of structural equations which imply the long-run exclusion restrictions on the impulse responses which are used to identify the model. A recent contribution shows a method to impose the sufficient conditions on the structural equations and to estimate them by instrumental variables (IV). This method has the advantage that it can be combined with a new method for sign restrictions which can be cast in an IV framework. This paper shows that the sufficient conditions which imply the two long-run exclusion restrictions in a SVAR taken from the literature imply other long-run exclusion restrictions as well which are not part of the identifying assumptions. In this case, this method is not suitable. This paper shows how to impose the two long-run exclusion restrictions directly on the structural equations of the model on each draw in sign restrictions which utilizes the IV method.

A remark on “Study of a Leslie-Gower predator-prey model with prey defense and mutual interference of predators” [Chaos, Solitons & Fractals 120 (2019) 1–16

Abstract In Mishra et al. (2019, [12]) a classical three-species modified Leslie-Gower system is considered, with mutual interference and prey-defense. The existence of a globally attracting invariant set is established for the system, under certain parametric restrictions. We show that the claimed invariant set is not globally attracting, and that finite time blow-up can occur for sufficiently large or small initial data. We further show that the invariant set cannot contain any interior equilibrium.

Bayesian predictive distribution for a Poisson model with a parametric restriction

Predictive probability estimation for a Poisson distribution is addressed when the parameter space is restricted. The Bayesian predictive probability against the prior on the restricted space is compared with the non-restricted Bayes predictive probability. It is shown that the former predictive probability dominates the latter under some conditions when the predictive probabilities are evaluated by the risk function relative to the Kullback-Leibler divergence. This result is proved by first showing the corresponding dominance result for estimating the restricted parameter and then translating it into the framework of predictive probability estimation.

Thermodynamic constraints and the use of energy-dependent CES-production functions A cautionary comment

Particularly in the context of energy and climate policy models, CES production functions are used as a basis for deriving sustainable development paths. Of crucial importance here is the reduction of the energy intensity of production processes with the help of substitution processes away from energy to other inputs. The modeling of these substitution processes must, of course, comply with the laws of physics. Therefore, the CES function is often used because it is supposed to satisfy thermodynamic laws. This is assumed to be met if the elasticity of substitution between energy inputs and other non-energy inputs is less than 1. The following commentary is meant to show that this specification is only a necessary pre-condition for fulfilling the thermodynamic laws. The permissible values of the other parameters of the CES- production function are subject to additional restrictions. Using an empirical example, the thermodynamic parameter restriction space for an aggregated production function of the English economy are presented. The consideration of thermodynamic limits can also be included directly into the design of production functions. An analysis of the linear-exponential production function derives various characteristics relevant to policy analysis. It is a priori not possible to decide which approach is preferable. Future empirical studies can help to clarify this question.

Optical solitons to Kundu–Mukherjee–Naskar model with modified simple equation approach

The Kundu–Mukherjee–Naskar model is examined to uncover quite important optical solitons in (2 + 1)-dimensions of its. Dark, bright and also singular solitons in additionally singular periodic solutions are yield by modified simple equation technique with parameter restrictions.

Highly dispersive optical solitons with non-local nonlinearity by extended Jacobi's elliptic function expansion

The work on this paper focuses on the retrieval of highly dispersive optical solitons that maintain non-local nonlinearity. The extended version of Jacobi's elliptic function expansion successfully yielded bright and singular as well a couple of combo optical solitons. The parameter restrictions, for the existence of such solitons, naturally emerged from the scheme.