Gaussian Term Research Articles

Lattice thermal conductivity of filled skutterudites: An anharmonicity perspective

We report a phenomenological model to calculate the high-temperature lattice thermal conductivity of filled skutterudite antimonides. The model needs no phonon resonant scattering terms. Instead, we assume that umklapp processes dominate the high-temperature phonon scattering. In order to represent the anharmonicity introduced by the filling atom, we introduce a Gaussian term into the relaxation time of the umklapp process. The developed model agrees remarkably well with the experimental results of REfCo4Sb12 and REfFe4Sb12 (RE = Yb, Ba, and Ca) alloys. To further test the validity of our model, we calculate the lattice thermal conductivity of nanostructured or multi-filled skutterudites. The calculation results are also in good agreement with experiment, increasing our confidence in the developed anharmonicity model.

FAST SWAPTION PRICING IN GAUSSIAN TERM STRUCTURE MODELS

We propose a fast and accurate numerical method for pricing European swaptions in multifactor Gaussian term structure models. Our method can be used to accelerate the calibration of such models to the volatility surface. The pricing of an interest rate option in such a model involves evaluating a multidimensional integral of the payoff of the claim on a domain where the payoff is positive. In our method, we approximate the exercise boundary of the state space by a hyperplane tangent to the maximum probability point on the boundary and simplify the multidimensional integration into an analytical form. The maximum probability point can be determined using the gradient descent method. We demonstrate that our method is superior to previous methods by comparing the results to the price obtained by numerical integration.

Towards an understanding of the roles of visual areas MT and MST in computing speed.

Towards an understanding of the roles of visual areas MT and MST in computing speed.

Non-Markov Gaussian Term Structure Models: The Case of Inflation*

Standard Gaussian term structure models impose the Markov property: the conditional mean is a function of the risk factors. We relax this assumption and consider models where yields are linear in the conditional mean (but not in the risk factors). To illustrate, yields should span expected inflation but not inflation. Second, expected and surprise yield changes can have opposite contemporaneous effects on expected inflation. Third, the survey forecasts and inflation rate can both be in the state. These three features are inconsistent with the Markov assumption. These effects matter empirically in the USA and in Canada.

Affine Principal-Component-Based Term Structure Model

We present an affine multifactor Gaussian term structure model, where we let factors be principal components of yields. Taking forward the affine-yield idea presented in Duffie and Kan (1996) we derive general expressions for the coefficients of a multidimensional affine Gaussian stochastic process given an exogenous matrix of loadings of selected yields on the state variables.

Langevin description of gauged scalar fields in a thermal bath

We study the dynamics of the oscillating gauged scalar field in a thermal bath. A Langevin type equation of motion of the scalar field, which contains both dissipation and fluctuation terms, is derived by using the real-time finite temperature effective action approach. The existence of the quantum fluctuation-dissipation relation between the non-local dissipation term and the Gaussian stochastic noise terms is verified. We find the noise variables are anti-correlated at equal-time. The dissipation rate for the each mode is also studied, which turns out to depend on the wavenumber.

Convergence of linear functionals of the Grenander estimator under misspecification

Under the assumption that the true density is decreasing, it is well known that the Grenander estimator converges at rate $n^{1/3}$ if the true density is curved [Sankhy\={a} Ser. A 31 (1969) 23-36] and at rate $n^{1/2}$ if the density is flat [Ann. Probab. 11 (1983) 328-345; Canad. J. Statist. 27 (1999) 557-566]. In the case that the true density is misspecified, the results of Patilea [Ann. Statist. 29 (2001) 94-123] tell us that the global convergence rate is of order $n^{1/3}$ in Hellinger distance. Here, we show that the local convergence rate is $n^{1/2}$ at a point where the density is misspecified. This is not in contradiction with the results of Patilea [Ann. Statist. 29 (2001) 94-123]: the global convergence rate simply comes from locally curved well-specified regions. Furthermore, we study global convergence under misspecification by considering linear functionals. The rate of convergence is $n^{1/2}$ and we show that the limit is made up of two independent terms: a mean-zero Gaussian term and a second term (with nonzero mean) which is present only if the density has well-specified locally flat regions.

Momentum and the Term Structure of Interest Rates

A vast literature reports excess returns to momentum strategies across many financial asset classes. However, no study examines trading rules based on price history along individual government-bond term structures — that is, with respect to duration buckets across the curve — as opposed to across sovereign markets or individual term structures as a whole over time. Under duration-neutral and long-only constraints as well as low trading costs, this paper reports excess annualized returns of up to 120 basis points and information ratios as high as 0.79 using U.S. Treasury total return data from December 1996 through July 2013. Given a corresponding long-short strategy with no absolute duration risk, excess returns and information ratios are up to 207 basis points and 1.01, respectively. Unlike momentum strategies in some other asset classes, the excess return distributions are positively skewed, and momentum loads, if in any way, favorably on broad risk factors. Returns correlate to a degree with portfolios based on instantaneous forward term premium estimates, in turn derived from a set of Gaussian arbitrage-free affine term structure models. However, substantial variance remains unexplained, the betas are less than one, and the alphas are meaningfully positive. A caveat is that underlying behavioral explanations for momentum are lacking in the context of the U.S. Treasury market.

Stability and Bifurcation Analysis of a Singular Delayed Predator-Prey Bioeconomic Model with Stochastic Fluctuations

This study investigates a singular delayed predator-prey bioeconomic model with stochastic fluctuations, which is described by differential-algebraic equations because of economic factors. The interior equilibrium of the singular delayed predator-prey bioeconomic model switches from being stable to unstable and then back to being stable, with the increase in time delay. The critical values for stability switches and Hopf bifurcations can be analytically determined. Subsequently, the effect of a fluctuating environment on the singular stochastic delayed predator-prey bioeconomic model obtained by introducing Gaussian white noise terms to the aforementioned deterministic model system is discussed. The fluctuation intensity of the population and harvest effort are calculated by Fourier transform method. Numerical simulation results are presented to verify the effectiveness of the conclusions.

Calibration of an Integrated Land-Use and Transportation Model Using Maximum-Likelihood Estimation

The focus of this work is calibration of the land-use module of an integrated land-use and transportation model (ILUTM). The calibration task involves estimating key parameters that dictate the output of the land-use module. Hence, an algorithm based on maximum-likelihood estimation (MLE) is developed for calibration. Furthermore, the observed values of the outputs from the land-use module are assumed to admit a Gaussian error. The ILUTM methodology used here is TRANUS which is used to model the city of Grenoble in France. The aforementioned algorithm is then applied to calibrate the land-use module of the Grenoble model. The covariance of the Gaussian error term is assumed to be unknown. It is represented as a function of the land-use module inputs and "hyperparameters.â' The resulting MLE optimization problem has 111 parameters to be estimated, 90 of which are land use parameters and 21 are hyperparameters of the Gaussian covariance kernel. The performance of the proposed calibration methodology is then compared to the traditional calibration techniques used for land use and transportation models, when applied to the Grenoble land-use model. It is observed that the proposed method outperforms the traditional technique when compared based upon a given quantity of interest.

Identification and Estimation of Gaussian Affine Term Structure Models with Regime Switching

We establish that [1]’s parameters are universally unidentified and a subset of their parameterization is over identified. As a solution to the problem with the identifiability, we propose a new representation of double-regime three-factor GDTSMs whose parameters are just-identified when the number of the pricing-with-error yields equals 2. This new parametrization has another advantage over [2] in that we can back out Q parameters and P parameters separately and make the estimation of structural parameters easier. Finally, we show that regime-switching three-factor arbitrage-free dynamic Nelson-Siegel model is a restricted special case of our model.

Dynamical analysis of a delayed singular prey–predator economic model with stochastic fluctuations

This article studies a delayed singular prey–predator economic model with stochastic fluctuations, which is described by differential‐algebraic equations due to a economic theory. Local stability and Hopf bifurcation condition are described on the delayed singular prey–predator economic model within deterministic environment. It reveals the sensitivity of the model dynamics on gestation time delay. A phenomenon of Hopf bifurcation occurs as the gestation time delay increases through a certain threshold. Subsequently, a singular stochastic prey–predator economic model with time delay is obtained by introducing Gaussian white noise terms to the above deterministic model system. The fluctuation intensity of population and harvest effort are calculated by Fourier transforms method. Numerical simulations are carried out to substantiate these theory analysis. © 2013 Wiley Periodicals, Inc. Complexity 19: 23–29, 2014

A study of the solution to the Riccati equation in term structure modelling

We study numerical (i.e. approximate) and analytical (i.e. exact) solutions to the system of Riccati ordinary differential equations (RODE) used in estimating the class of Gaussian affine term structure models (ATSM). We base our study on accuracy and convergence time, and find that usage of the approximate solution and exact solution to the RODE yield similar accuracy. Our results are consistent with the no-arbitrage condition specified in ATSM. We also show that exact solutions, when available, lead to faster convergence times than approximate solutions.

Macroeconomic and Monetary Policy Surprises and the Term Structure of Interest Rates

The no-arbitrage affine Gaussian term structure model is used to analyse the impact of macroeconomic surprises on the nominal and the real term structure in the euro area and in the United States. We find that nominal rates are affected by surprises in economic growth, the labour market and the economic outlook in the United States, and above all by surprises in inflation in the euro area. As far as real rates are concerned, we find that they are not affected by macroeconomic surprises in the United States, but they are by surprises in inflation and monetary policy in the euro area. Inflation expectations in both areas are not systematically influenced by monetary policy surprises. In the United States forward inflation risk premia became sizeable around the start of the financial crisis at the end of the last decade and increased considerably just before the adoption of the first unconventional monetary policy measures in March 2009. By contrast, in the euro area forward inflation risk premia remained unchanged even after the adoption of the unconventional monetary policy measures in October 2008 and May 2010. In both areas long-term inflation expectations have been well anchored over the past years.

JFEC Invited Paper: Gaussian Macro-Finance Term Structure Models with Lags

This paper develops a new family of Gaussian macro-dynamic term structure models (MTSMs) in which bond yields follow a low-dimensional factor structure and the historical distribution of bond yields and macroeconomic variables is characterized by a vector-autoregression with order p > 1. Most formulations of MTSMs with p > 1 are shown to imply a much higher dimensional factor structure for yields than what is called for by historical data. In contrast, our \asymmetric arbitrage-free MTSM gives modelers the exibility to match historical lag distributions with p > 1 while maintaining a parsimonious factor representation of yields. Using our canonical family of MTSMs we revisit: (i) the impact of no-arbitrage restrictions on the joint distribution of bond yields and macro risks, comparing models with and without the restriction that macro risks are spanned by yield curve information; and (ii) the identication of the policy parameters in Taylor-style monetary policy rules within MTSMs with macro risk factors and lags.

An evaluation of alternative methods used in the estimation of Gaussian term structure models

This paper provides an evaluation of five methods, proposed in the literature, for extracting factors used in the estimation of Gaussian affine term structure models. We assert that irrespective of the method used for extracting state variables, cross-sectional and serial correlations exist in measurement errors. However, using a simulation design which is consistent with the data, we show that parameter estimation using the Kalman filter and the model-free method are quite precise in the presence of serial and cross-sectional correlations in the error term, and, in the presence of different measurement errors, the Kalman filter demonstrates strong empirical tractability.

A Tractable Framework for Zero-Lower-Bound Gaussian Term Structure Models

When nominal interest rates are near their zero lower bound (ZLB), as in many developed economies at the time of writing, it is theoretically untenable to apply the popular class of Gaussian affine term structure models (GATSMs) given their inherent material probabilities of negative interest rates. Hence, I propose a new and tractable modification for GATSMs that enforces the ZLB, and which approximates the fully arbitrage-free but much less tractable framework proposed in Black (1995). I apply my framework to United States yield curve data, with robust estimation via the iterated extended Kalman filter, and first show that the two-factor results are very similar to those from a comparable Black model. I then estimate two- and three-factor models with longer-maturity data sets to illustrate that my ZLB framework can readily be applied in circumstances that would be computationally burdensome or infeasible within the Black framework.

Simple effective interaction: infinite nuclear matter and finite nuclei

The mean field properties and equation of state for asymmetric nuclear matter are studied using a simple effective interaction, which has a single finite-range Gaussian term. The study of finite nuclei with this effective interaction is done by constructing a quasilocal energy density functional for which the single-particle equations take the form of Skryme–Hartree–Fock equations. The predictions of binding energies and charge radii of spherical nuclei are found to be compatible with the results of successful mean field models, as well as with the experimental data.

Estimating Shadow-Rate Term Structure Models with Near-Zero Yields

Standard Gaussian term structure models have often been criticized for not ruling out negative nominal interest rates, but this flaw has been especially conspicuous with interest rates near zero in many countries. We provide a tractable means to estimate an alternative Gaussian shadow-rate dynamic term structure model that enforces the zero lower bound on bond yields. We illustrate this model by estimating one-, two-, and three-factor shadow-rate models on a sample of positive and near-zero Japanese bond yields. We find that the level of the shadow rate is sensitive to model fit and specification, including the number of factors employed.

Effects of non-Gaussian noise on the dynamical properties of a logistic system

The dynamical properties of a tumor cell growth system described by the logistic system with coupling between non-Gaussian and Gaussian noise terms are investigated. The effects of the nonextensive index q on the stationary properties and the transient properties are discussed, respectively. The results show that the nonextensive index q can induce the tumor cell numbers to decrease greatly in the case of q > 1. Moreover, the switch from the steady stable state to the extinct state is speeded up as the increases of q, and the tumor cell numbers can be more obviously restrained for a large value of q. The numerical results are found to be in basic agreement with the theoretical predictions.