Size Of Jumps Research Articles

Local spline refinement driven by fault jump estimates for scattered data approximation

We present new fault jump estimates to guide local refinement in surface approximation schemes with adaptive spline constructions. The proposed approach is based on the idea that, since discontinuities in the data should naturally correspond to sharp variations in the reconstructed surface, the location and size of jumps detected in the input point cloud should drive the mesh refinement algorithm. To exploit the possibility of inserting local meshlines in one or the other coordinate direction, as suggested by the jump estimates, we propose a quasi-interpolation (QI) scheme based on locally refined B-splines (LR B-splines). Particular attention is devoted to the construction of the local operator of the LR B-spline QI scheme, which properly adapts the spline approximation according to the nature and density of the scattered data configuration. A selection of numerical examples outlines the performance of the method on synthetic and real datasets characterized by different geographical features.

Orlicz risks for assessing stochastic streamflow environments: a static optimization approach

This study applies novel risk measures, called Orlicz risks, to the risk and uncertainty evaluation of the streamflow discharge as a primary driver of hydrological and hydraulic processes of interest in civil and environmental engineering. We consider the mixed moving average process governing the discharge whose statistics are explicitly represented as some product of a time-scale characterizing the flow attenuation and a jump moment governing the size and frequency of jumps. The classical Orlicz risks are extended so that not only the upper tail risk but also the lower one of the jump size and attenuation of the discharge can be evaluated within a single mathematical framework. Further, the risk and uncertainty can be individually quantified in a tractable manner by the proposed Orlicz risks. Computing the Orlicz risks reduces to solving a pair of novel static optimization problems that are solvable semi-analytically. The risk and uncertainty involved in the streamflow dynamics can be consistently evaluated by specifying few user-dependent parameters. The associated Radon–Nikodym derivatives as the worst-case model uncertainties are obtained as byproducts. Sufficient conditions for the well-posedness of the Orlicz risks are discussed and numerical algorithms for computing them are presented. We finally apply the proposed framework to a statistical analysis of the streamflow discharge time series data collected at mountainous river environments.

Nonparametric Bayesian modeling for baseline hazard functions

Survival analysis is primarily used to identify the time-to-event for events of interest. The Cox proportional hazards model takes advantage that it accounts for the proportionate risks of covariates without estimating exact baseline hazards. However, estimation of exact hazard distribution is always accompanied by estimating baseline hazard function as well as regression parameters. In this study, we adopted nonparametric Bayesian hierarchical model with flexible priors in estimating cumulative baseline hazard function. We assume a monotone step function for the cumulative baseline hazard function, where the number, size, and location of jumps are random. By Estimating the step function through stick-breaking construction, we can obtain a totally data-driven step function.

Stochastic deterioration modelling of sidewalk performance using compound poisson processes

ABSTRACT Pedestrian sidewalk plays an increasingly important role in urban transportation. Due to the traditional misconception of it being an infrastructure class of low risk, the current sidewalk asset management still largely relies on experiences and personal judgment. To promote rational asset management, the authors have recently developed two performance indicators namely, the maintenance repair index (MRI) and the sidewalk condition index (SCI). This paper advances the effort by developing two deterioration models using a compound Poisson process (CPP), which consists of a nonhomogeneous Poisson process for the jumping time and a Weibull distribution for the jumping size. Based on a real-life sidewalk defects database, the models also consider the heterogeneity of the sidewalks by including asset attributes such as sidewalk service age, foundation soil type, sidewalk size, pedestrian density, and intensity of construction activities in the vicinity of a sidewalk. The modelling approach presented in the paper – particularly the considerations in the selection of CPP model, the Bayesian statistical inference method, and the model validation process – serves as an excellent example for stochastic deterioration modelling for risk-informed infrastructure asset management.

Exact targeting of gibbs distributions using velocity-jump processes

This work introduces and studies a new family of velocity jump Markov processes directly amenable to exact simulation with the following two properties: (i) trajectories converge in law, when a time-step parameter vanishes, towards a given Langevin or Hamiltonian dynamics; (ii) the stationary distribution of the process is always exactly given by the product of a Gaussian (for velocities) by any target log-density. The simulation itself, in addition to the computability of the gradient of the log-density, depends on the knowledge of appropriate explicit upper bounds on lower order derivatives of this log-density. The process does not exhibit any velocity reflections (maximum size of jumps can be controlled) and is suitable for the ’factorization method’. We provide rigorous mathematical proofs of the convergence towards Hamiltonian/Langevin dynamics when the time step vanishes, and of the exponentially fast convergence towards the target distribution when a suitable noise on velocities is present. Numerical implementation is detailed and illustrated.

The Packing Chromatic Number of Different Jump Sizes of Circulant Graphs

The packing chromatic number χ_{p}(G) of a graph G = (V,E) is the smallest integer k such that the vertex set V(G) can be partitioned into disjoint classes V1 ,V2 ,...,Vk , where vertices in Vi have pairwise distance greater than i. In this paper, we compute the packing chromatic number of circulant graphs with different jump sizes._{}

A generalized finite difference method for solving elasticity interface problems

In this paper, a generalized finite difference method (GFDM) is proposed to solve the elasticity interface problem. This method turns the original elasticity interface problem to be some coupled non-interface subproblems. A large sparse matrix can be yielded by those subproblems. Since this method makes the interface become a part of boundaries of subproblems, it can deal well with problems with complex geometrical interfaces. Moreover, this method can also deal well with the interface conditions with derivatives, because the GFDM uses a linear summation of nearby nodal values to express the derivatives of unknown variables. Numerical examples are provided to verify the accuracy and stability of the proposed method for elasticity interface problems. They show that the H1 error of the method has the almost same convergence rate as the L2error and the size of jumps in the interface conditions only has a little effect on the stability of the proposed method.

Rodeo or Ascot: which hat to wear at the crypto race?

This paper sheds light on the dynamics of the cryptocurrency (CC) sector. By modeling its dynamics via a stochastic volatility with correlated jumps (SVCJ) model in combination with several rolling windows, it is possible to capture the extreme ups and downs of the CC market and to understand its dynamics. Through this approach, we obtain time series for each parameter of the model. Even though parameter estimates change over time and depend on the window size, several recurring patterns are observable which are robust to changes of the window size and supported by clustering of parameter estimates: during bullish periods, volatility stabilizes at low levels and the size and volatility of jumps in mean decreases. In bearish periods though, volatility increases and takes longer to return to its long-run trend. Furthermore, jumps in mean and jumps in volatility are independent. With the rise of the CC market in 2017, a level shift of the volatility of volatility occurred. All codes are available on this http URL.

Sequential Hypothesis Testing in Machine Learning, and Crude Oil Price Jump Size Detection

ABSTRACT In this paper, we present a sequential hypothesis test for the detection of the distribution of jump size in Lévy processes. Infinitesimal generators for the corresponding log-likelihood ratios are presented and analysed. Bounds for infinitesimal generators in terms of super-solutions and sub-solutions are computed. This is shown to be implementable in relation to various classification problems for a crude oil price data set. Machine and deep learning algorithms are implemented to extract a specific deterministic component from the data set, and the deterministic component is implemented to improve the Barndorff-Nielsen & Shephard model, a commonly used stochastic model for derivative and commodity market analysis.

STOCHASTIC VOLATILITY MODEL WITH CORRELATED JUMP SIZES AND INDEPENDENT ARRIVALS

In light of recent empirical research on jump activity, this article study the calibration of a new class of stochastic volatility models that include both jumps in return and volatility. Specifically, we consider correlated jump sizes and both contemporaneous and independent arrival of jumps in return and volatility. Based on the specifications of this model, we derive a closed-form relationship between the VIX index and latent volatility. Also, we propose a closed-form logarithmic likelihood formula by using the link to the VIX index. By estimating alternative models, we find that the general counting processes setting lead to better capturing of return jump behaviors. That is, the part where the return and volatility jump simultaneously and the part that jump independently can both be captured. In addition, the size of the jumps in volatility is, on average, positive for both contemporaneous and independent arrivals. However, contemporaneous jumps in the return are negative, but independent return jumps are positive. The sub-period analysis further supports above insight, and we find that the jumps in return and volatility increased significantly during the two recent economic crises.

Futures-Trading Activity and Jump Risk: Evidence From the Bitcoin Market

This paper examines the effects of futures trading on the jump risk in the Bitcoin market. We use a nonparametric method to detect Levy-type jumps in Bitcoin prices and obtain jump risk measures (jump intensity and jump size) of big and small jumps by using 5-minute high-frequency data, and document that Bitcoin has obvious features of Levy jumps, i.e., prices include both big jumps and small jumps, and the jump risk is time-varying. We then investigate the changes of these jump risk measures before and after the introduction of the Bitcoin futures, and we find that the jump size of big and small jumps decreases after the introduction of Bitcoin futures, while the big jump intensity increases. Further, we examine whether greater futures-trading activity (volume and open interest) is associated with greater Bitcoin jump risk and document that, on the one hand, there exists bidirectional causality between unexpected volume and jump intensity and size of Bitcoin and the impulse response function analysis show that the shocks have temporary increasing effects, and the speculative trading in the futures market will increase the jump risk. On the other hand, unexpected open interest Granger causes jump risk but the inverse is not true, indicating that investors are unlikely to hedge jump risk by using Bitcoin futures. These findings disclose the fact that the hedging function of the Bitcoin futures does not work well and the functions of Bitcoin futures need to be further improved.

Impact of portfolio flows and heterogeneous expectations on FX jumps: Evidence from an emerging market

Motivated by the recent currency crisis in Turkey, we investigate the role of portfolio flows and heterogeneous expectations on the high frequency stochastic jump behavior of the US dollar value against the Turkish lira, one of the most traded emerging market currencies in the world. We group the detected jumps into different types with respect to their direction (up and down) and timing (local and off-shore trading hours). For each type of jumps, we examine their relation with portfolio flows (in the form of equity and bond flows, and carry trade activity), and dispersion in beliefs for the future exchange rate level and key macroeconomic variables. We find that inflows to both equity and bond markets, and increasing carry trade activity significantly reduce the size of jumps and (partially) their intensity. On the other hand, heterogeneous expectations for the future exchange rate level, consumer price index and gross domestic product are found to increase the number of jumps and the average jump size.

Simulation of Drop-Size Distribution During Dropwise and Jumping Drop Condensation on a Vertical Surface: Implications for Heat Transfer Modeling.

Accurate models for condensation heat transfer are necessary to improve condenser design. Drop-size distribution is an important aspect of heat transfer modeling that is difficult to measure for small drop sizes. The present work uses a numerical simulation of condensation which incorporates the possibility of coalescence and coalescence-induced jumping over a range of drop sizes. Results of the simulation are compared with previous theoretical models and the impact of the assumptions used in those models is explored. In particular, previous drop-size distribution models may predict heat transfer rates less accurately for high contact angles and for coalescence-induced jumping since coalescence occurs over a range of drop sizes and does not always result in departure. The influence of various input parameters (nucleation site distribution approach, nucleation site density, contact angle, maximum drop size, heat transfer modeling to individual drops, and minimum jumping size) on the drop-size distribution and overall heat transfer rate is explored. Assignment of the nucleation site spatial distribution and heat transfer model affect both the drop-size distribution and predicted overall heat transfer rate. Results from the simulation suggest that, when the contact angle is large (as on superhydrophobic surfaces) and no coalescence-induced jumping occurs, the heat transfer may not be as sensitive to the maximum drop-size as previously supposed. Furthermore, this work suggests that when coalescence-induced jumping occurs, reducing the maximum drop size may not always increase heat transfer since drops similar in size to those removed by coalescence-induced jumping can contribute significantly to the overall heat transfer rate.

The Hall–Petch Relationship for the Sizes of Deformation Jumps in Metals

The paper presents an attempt to use the Hall–Petch relationship to relate the yield strength of copper and titanium in three different states (initial, annealed, and after equal-channel angular pressing) to the sizes of nano- and micrometer deformation jumps measured using a precision interferometric technique. It is shown that, upon a compression strain near the yield point, one can observe six levels of deformation with three nano- and three micrometer sizes of deformation jumps from 1–2 nm to 20–35 μm. Each of the six structural states of metals is characterized by its own set of deformation jump sizes. Dependences of the yield strengths of copper and titanium on the jump sizes L–1/2 are constructed, and the general regularities and features of deformation jumps for each of the metals in different structural states are discussed.

Cоотношение Холла-Петча для размеров скачков деформации металлов

AbstractThe paper presents an attempt to use the Hall–Petch relationship to relate the yield strength of copper and titanium in three different states (initial, annealed, and after equal-channel angular pressing) to the sizes of nano- and micrometer deformation jumps measured using a precision interferometric technique. It is shown that, upon a compression strain near the yield point, one can observe six levels of deformation with three nano- and three micrometer sizes of deformation jumps from 1–2 nm to 20–35 μm. Each of the six structural states of metals is characterized by its own set of deformation jump sizes. Dependences of the yield strengths of copper and titanium on the jump sizes L ^–1/2 are constructed, and the general regularities and features of deformation jumps for each of the metals in different structural states are discussed.

The Sizes of Jumps and Levels of Deformation of Metals

It is proposed to characterize levels of deformation by a size of its jumps, which can be observed when the strain rate is accurately measured in experiments with load that is constant or defined according a certain law. At the micro- and nanometer scales, the strain rate was measured and the deformation jumps were computed for copper, lead, and tin using a precision interferometric method. A correlation of the size of jumps with the Burgers vector of dislocations in metals was shown, and hypotheses about ensembles of dislocations participating in the formation of a deformation jump are made.

Testing CEV stochastic volatility models using implied volatility index data

We test the goodness-of-fit of stochastic volatility (SV) models using the implied volatility index of the KOSPI200 options (VKOSPI). The likelihood ratio tests reject the Heston and Hull–White SV models, whether or not they include jumps. Our estimation results advocate the unconstrained constant elasticity of variance (CEV) model with return jumps for describing the physical-measure dynamics of the spot index. The sub-period analysis shows that there was a significant increase in the size and frequency of jumps during the crisis period, when compared to those in the normal periods.

Generalized Master Equations for Random Walks with Time-Dependent Jump Sizes

In this work, we develop a unified generalized master equation (GME) framework that extends the theory of continuous time random walks to include the cases when the jump sizes may have a delayed de...

Размеры скачков и уровни деформации металлов

AbstractIt is proposed to characterize levels of deformation by a size of its jumps, which can be observed when the strain rate is accurately measured in experiments with load that is constant or defined according a certain law. At the micro- and nanometer scales, the strain rate was measured and the deformation jumps were computed for copper, lead, and tin using a precision interferometric method. A correlation of the size of jumps with the Burgers vector of dislocations in metals was shown, and hypotheses about ensembles of dislocations participating in the formation of a deformation jump are made.

Macroeconomic Uncertainty Through the Lens of Professional Forecasters

ABSTRACTWe analyze the evolution of macroeconomic uncertainty in the United States, based on the forecast errors of consensus survey forecasts of various economic indicators. Comprehensive information contained in the survey forecasts enables us to capture a real-time measure of uncertainty surrounding subjective forecasts in a simple framework. We jointly model and estimate macroeconomic (common) and indicator-specific uncertainties of four indicators, using a factor stochastic volatility model. Our macroeconomic uncertainty estimates have three major spikes has three major spikes aligned with the 1973–1975, 1980, and 2007–2009 recessions, while other recessions were characterized by increases in indicator-specific uncertainties. We also show that the selection of data vintages affects the estimates and relative size of jumps in estimated uncertainty series. Finally, our macroeconomic uncertainty has a persistent negative impact on real economic activity, rather than producing “wait-and-see” dynamics.