Reliability evaluation subject to assured accuracy rate and time for stochastic unreliable-node computer networks

In many real-life networks such as computer networks, branches and nodes have multi-state capacity, lead time, and accuracy rate. The network with unreliable nodes is more complex to evaluate the reliability because node failure results in the disabled of adjacent branches. Such a network is named a stochastic unreliable-node computer network (SUNCN). Under the strict assumption that each component (branch and node) has a deterministic capacity, the quickest path (QP) problem is to find a path sending a specific amount of data with minimum transmission time. The accuracy rate is a critical index to measure the performance of a computer network because some packets are damaged or lost due to voltage instability, magnetic field effects, lightning, etc. Subject to both assured accuracy rate and time constraints, this paper extends the QP problem to discuss the system reliability of an SUNCN. An efficient algorithm based on a graphic technique is proposed to find the minimal capacity vector meeting such constraints. System reliability, the probability to send a specific amount of data through multiple minimal paths subject to both assured accuracy rate and time constraints, can subsequently be computed.     

C338. Misspecified location and scale. 111. the use of S2

The observed high kurtosis of stock market returns and other variables of a speculative nature has aroused interest in stable law distributions. This paper makes the point that most historical findings that returns indeed follow stable laws may have been caused by conditional heteroskedasticity. This presumption is enhanced by Monte Carlo simulations.     

Numerical computation of multivariate t-probabilities with application to power calculation of multiple contrasts

A new method to calculate the multivariate t-distribution is introduced. We provide a series of substitutions, which transform the starting q-variate integral into one over the (q—1)-dimensional hypercube. In this situation standard numerical integration methods can be applied. Three algorithms are discussed in detail. As an application we derive an expression to calculate the power of multiple contrast tests assuming normally distributed data.     

Forecasting energy futures volatility with threshold augmented heterogeneous autoregressive jump models

Abstract

This study forecasts the volatility of two energy futures markets (oil and gas), using high-frequency data. We, first, disentangle volatility into continuous volatility and jumps. Second, we apply wavelet analysis to study the relationship between volume and the volatility measures for different horizons. Third, we augment the heterogeneous autoregressive (HAR) model by nonlinearly including both jumps and volume. We then propose different empirical extensions of the HAR model. Our study shows that oil and gas volatilities nonlinearly depend on public information (jumps), private information (continuous volatility), and trading volume. Moreover, our threshold augmented HAR model with heterogeneous jumps and continuous volatility outperforms HAR model in forecasting volatility.     

On the choice of the mesh for the analysis of geostatistical data using R-INLA

Abstract

Many methods used in spatial statistics are computationally demanding, and so, the development of more computationally efficient methods has received attention. A important development is the integrated nested Laplace approximation method which is carry out Bayesian analysis more efficiently This method, for geostatistical data, is done considering the SPDE approach that requires the creation of a mesh overlying the study area and all the obtained results depend on it. The impact of the mesh on inference and prediction is investigated through simulations. As there is no formal procedure to specify it, we investigate a guideline to create an optimal mesh.     

A multifactor transformed diffusion model with applications to VIX and VIX futures

Abstract

Transformed diffusions (TDs) have become increasingly popular in financial modeling for their model flexibility and tractability. While existing TD models are predominately one-factor models, empirical evidence often prefers models with multiple factors. We propose a novel distribution-driven nonlinear multifactor TD model with latent components. Our model is a transformation of a underlying multivariate Ornstein–Uhlenbeck (MVOU) process, where the transformation function is endogenously specified by a flexible parametric stationary distribution of the observed variable. Computationally efficient exact likelihood inference can be implemented for our model using a modified Kalman filter algorithm and the transformed affine structure also allows us to price derivatives in semi-closed form. We compare the proposed multifactor model with existing TD models for modeling VIX and pricing VIX futures. Our results show that the proposed model outperforms all existing TD models both in the sample and out of the sample consistently across all categories and scenarios of our comparison.     

Markov chain models for multivariate repeated binary data analysis

Repeated categorical outcomes frequently occur in clinical trials. Muenz and Rubinstein (1985) presented Markov chain models to analyze binary repeated data in a breast cancer study. We extend their method to the setting when more than one repeated outcome variable is of interest. In a randomized clinical trial of breast cancer, we investigate the dependency of toxicities on predictor variables and the relationship among multiple toxic effects.     

Large Sample Properties of ML Estimator of the Parameters of Multivariate O–U Random Fields

Computer modeling is having a profound effect on scientific research, replacing direct physical experimentation by computer simulation of complex models. In this research, the computer output, X(t), is assumed to be a multivariate, three-dimensional (time) Ornstein-Uhlenbeck (O–U) process with parametric covariance function. It is shown that the ML estimates of the parameters are strongly consistent and asymptotically normal when the observations are taken from a complete lattice, not necessarily equally spaced.     

Further results on the vecd operator and its applications

Abstract

In this paper, we consider the matrix vectorization operator termed the vecd operator, which has recently been introduced in the literature. This operator stacks up distinct elements of a symmetric matrix in a way that differs from that of the well-known vech operator; it stacks up not columns, but diagonals. We give further consideration to the vecd operator and related matrices, and derive their various useful properties. We provide some statistical applications of the vecd operator to illustrate its usefulness.