查看更多>>摘要：Volatility estimation is an important issue in certain aspects of the financial community, such as risk management and asset pricing. It is known that stock returns often exhibit volatility clustering and the tails of the distributions of these series are fatter than the normal distribution. As a response to the need of these issues, the high unconditional volatility of assets encourages the users to predict their price in an ever changing market environment. Our main focus in this paper is to study the behavior of returns and volatility dynamics of some general stochastic economic models. First, we apply the local polynomial kernel smoothing method based on nonparametric regression to estimate the mean and the variance of the returns. We then implement and develop an empirical likelihood procedure in terms of conditional variance on daily log returns for inference on the nonparametric stochastic volatility as well as to construct a confidence interval for the volatility function. It appears that the proposed algorithm is applicable to some popular financial models and represents a good fit for the behavior observed in the stock and cryptocurrency markets. Some numerical results in connection to real data on the S & P 500 index and highly volatile Bitcoin dataset are also illustrated. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：The error analysis of a proper orthogonal decomposition (POD) data assimilation (DA) scheme for the Navier-Stokes equations is carried out. A grad-div stabilization term is added to the formulation of the POD method. Error bounds with constants independent on inverse powers of the viscosity parameter are derived for the POD algorithm. No upper bounds in the nudging parameter of the data assimilation method are required. Numerical experiments show that, for large values of the nudging parameter, the proposed method rapidly converges to the real solution, and greatly improves the overall accuracy of standard POD schemes up to low viscosities over predictive time intervals. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：The generalized inverse Gaussian (GIG) Levy process is a limit of compound Poisson processes, including the stationary gamma process and the stationary inverse Gaussian process as special cases. However, fitting the GIG Levy process to data is computationally intractable due to the fact that the marginal distribution of the GIG Levy process is not convolution-closed. The current work reveals that the marginal distribution of the GIG Levy process admits a simple yet extremely accurate saddlepoint approximation. Particularly, we prove that if the order parameter of the GIG distribution is greater than or equal to -1, the marginal distribution can be approximated accurately - no need to normalize the saddlepoint density. Accordingly, maximum likelihood estimation is simple and quick, random number generation from the marginal distribution is straight-forward by using Monte Carlo methods, and goodness-of-fit testing is undemanding to perform. Therefore, major numerical impediments to the application of the GIG Levy process are removed. We demonstrate the accuracy of the saddlepoint approximation via various experimental setups. (C)& nbsp;2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：In this paper, we consider the linearly structured partial polynomial inverse eigenvalue problem (LPPIEP) of constructing the matrices Ai is an element of Rnxn for i = 0, 1, 2, ... , (k - 1) of specified linear structure such that the matrix polynomial P(lambda) = lambda kIn + n-ary sumation k-1 has the m (1 <= m <= kn) prescribed eigenpairs as its eigenvalues and eigenvectors. Many practical applications give rise to linearly structured matrix polynomials. Typical linearly structured matrices are symmetric, skew-symmetric, tridiagonal, diagonal, pentagonal, Hankel, Toeplitz, etc. Therefore, construction of the matrix polynomial with the aforementioned structures is an important but challenging aspect of the polynomial inverse eigenvalue problem (PIEP). In this paper, a necessary and sufficient condition for the existence of solution to this problem is derived. Additionally, we characterize the class of all solutions to this problem by giving the explicit expressions of the solutions. It should be emphasized that the results presented in this paper resolve some important open problems in the area of PIEP namely, the inverse eigenvalue problems for structured matrix polynomials such as symmetric, skew-symmetric, alternating matrix polynomials as pointed out by De Teran et al. (2015). Further, we study sensitivity of solution to the perturbation of the eigendata. An attractive feature of our solution approach is that it does not impose any restriction on the number of eigendata for computing the solution of LPPIEP. Towards the end, the proposed method is validated with various numerical examples on a spring mass problem.
查看更多>>摘要：In this paper we introduce a transformation of the center of gravity, variance and higher moments of fuzzy numbers into their possibilistic counterparts. We show that this transformation applied to the standard formulae for the computation of the center of gravity, variance, and higher moments of fuzzy numbers gives the same formulae for the computation of possibilistic moments of fuzzy numbers that were introduced by Carlsson and Fuller (2001) for the possibilistic mean and variance, and also the formulae for the calculation of higher possibilistic moments as presented by Saeidifar and Pasha (2009). We also present an inverse transformation to derive the formulae for standard measures of central tendency, dispersion, and higher moments of fuzzy numbers, from their possibilistic counterparts. This way a two-way transition between the standard and the possibilistic moments of fuzzy numbers is enabled. The transformation theorems are proven for a wide family of fuzzy numbers with continuous, piecewise monotonic membership functions. Fast computation formulae for the first four possibilistic moments of fuzzy numbers are also presented for linear fuzzy numbers, their concentrations and dilations. (C) 2022 The Author(s). Published by Elsevier B.V.
查看更多>>摘要：A new concept of fuzzy improved distribution function based on fuzzy ordering defined on the support set of a given random variable is introduced. A fuzzy improved random variable based on this distribution function is defined. The existence of such a fuzzy improved random variable follows from probability integral transformation. The order statistics based on the fuzzy ordering and fuzzy improved distribution function are considered and their distributions are studied. The need for fuzzy improved order statistics arises in reliability analysis of sensitive systems where the lifetimes of the components and the system are considered by taking into account some degree of smallness defined by membership function of a fuzzy set. Examples and graphical representations of fuzzy improved distribution functions are provided.(C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Condition number plays an important role in perturbation analysis, the latter is a tool to judge whether a numerical solution makes sense, especially for ill-posed problems. In this paper, perturbation analysis of the Tikhonov regularization of total least squares problem (TRTLS) is considered. The explicit expressions of normwise, mixed and componentwise condition numbers for the TRTLS problem are first presented. With the intermediate result, i.e. normwise condition number, we can recover the upper bound of TRTLS problem. To improve the computational efficiency in calculating the normwise condition number, a new compact and tight upper bound of the TRTLS problem is introduced. In addition, we also derive the normwise, mixed and componentwise condition numbers for TRTLS problem when the coefficient matrix, regularization matrix and right-hand side vector are all perturbed. We choose the probabilistic spectral norm estimator and the small-sample statistical condition estimation method to estimate these condition numbers with high reliability. Numerical experiments are provided to verify the obtained results. (C)& nbsp;2022 Elsevier B.V. All rights reserved.
Noeiaghdam, SamadAraghi, Mohammad Ali FariborziSidorov, Denis
13页
查看更多>>摘要：In this research, an efficient scheme is presented to validate the numerical results and solve the second kind integral equations (IEs). For this reason the homotopy perturbation method (HPM) is illustrated and the stochastic arithmetic is applied to implement the CESTAC1 method for solving IEs. The accuracy of method is shown by proving a main theorem. Also, the CADNA2 library is used instead of other usual softwares. Applying the mentioned method, the optimal approximation, iteration, validation of results and any numerical instability can be found whereas the floating-point arithmetic (FPA) has not these properties. Some examples are solved to determine the significance of applying the SA in place of the FPA.
查看更多>>摘要：We examine several of the normal-form multivariate polynomial rootfinding methods of Telen, Mourrain, and Van Barel and some variants of those methods. We analyze the performance of these variants in terms of their asymptotic temporal complexity as well as speed and accuracy on a wide range of numerical experiments. All variants of the algorithm are problematic for systems in which many roots are very close together. We analyze the performance on one such system in detail, namely the "devastating example "that Noferini and Townsend used to demonstrate instability of resultant-based methods. We demonstrate that the problems with the devastating example arise from having a large number of roots very close to each other. We also show that a small number of clustered roots does not cause numerical problems for these methods. We conjecture that the clustering of many roots is the primary source of problematic examples. (C) 2022 Elsevier B.V. All rights reserved.
查看更多>>摘要：Burst-b distance introduced by Wainberg and Wolf (1972) has been found to be useful for correction of multiple burst errors and multiple erasures. Villalba et al. (2016) have derived extended Reiger and Singleton bound for linear code with minimum burst-b distance d(b) and then present a class of Maximum Distance Separable (MDS) codes (named as C-b code). In this paper, we derive an upper bound on d(b) for any linear code and a lower bound on d(b) for constant burst-b weight linear codes. We also present the existence of linear code with burst-b distance d(b) - 1 from code with burst distance d(b). The cardinality of a linear code and the connection of linearly independent columns of the parity check matrix of any MDS code with the distance d(b) are also given. Further, we consider periodical burst error which is found in many communication channels and investigate periodical burst-detection and -correction capability of linear codes having distance d(b). Then, we do the same investigation for C-b and its dual code C-b(perpendicular to). Finally, we give decoding procedure for the code C-b in case of periodical burst errors. (C) 2022 Elsevier B.V. All rights reserved.
NSTL
Elsevier