SEMIFARMA-HYGARCH Modeling of Dow Jones Return Persistence

This paper analyzes the cyclical behavior of Dow Jones by testing the existence of long memory through a new class of semiparametric ARFIMA models with HYGARCH errors (SEMIFARMA-HYGARCH); this class includes nonparametric deterministic trend, stochastic trend, short-range and long-range dependence and long memory heteroscedastic errors. We study the daily returns of the Dow Jones from 1896 to 2006. We estimate several models and we find that the coefficients of the SEMIFARMA-HYGARCH model, including long memory coefficients for the equations of the mean and the conditional variance, are highly significant. The forecasting results show that the informational shocks have permanent effects on volatility and the SEMIFARMA-HYGARCH model has better performance over some other models for long and/or short horizons. The predictions from this model are also better than the predictions of the random walk model; accordingly, the weak efficiency assumption of financial markets seems violated for Dow Jones returns studied over a long period.     

Joint segmentation of multivariate Gaussian processes using mixed linear models

The joint segmentation of multiple series is considered. A mixed linear model is used to account for both covariates and correlations between signals. An estimation algorithm based on EM which involves a new dynamic programming strategy for the segmentation step is proposed. The computational efficiency of this procedure is shown and its performance is assessed through simulation experiments. Applications are presented in the field of climatic data analysis.     

Probability method for cryptanalysis of general multivariate modular linear equation

Finding the solution to a general multivariate modular linear equation plays an important role in cryptanalysis field. Earlier results show that obtaining a relatively short solution is possible in polynomial time. However, one problem arises here that if the equation has a short solution in given bounded range, the results outputted by earlier algorithms are often not the ones we are interested in. In this paper, we present a probability method based on lattice basis reduction to solve the problem. For a g...     

Joint order and parameter estimation of multivariate autoregressive models using multi-model partitioning theory

In this paper the multi-model partitioning theory is used for simultaneous order and parameter estimation of multivariate autoregressive models. Simulation experiments show that the proposed method successfully selects the correct model order and estimates the parameters accurately, in very few steps, even with a small sample size. They also show that the proposed method performs equally well when the complexity of the model is increased. The results are compared to those obtained using well-established order selection criteria. Finally, it is shown that the method is also successful in tracking model order changes, in real time.     

Joint modelling of multivariate longitudinal outcomes and a time-to-event: A nonlinear latent class approach

A joint model based on a latent class approach is proposed to explore the association between correlated longitudinal quantitative markers and a time-to-event. A longitudinal latent class model describes latent profiles of evolution of the latent process underlying the correlated markers. The latent process is linked to the markers by nonlinear transformations including parameters to be estimated. A proportional hazard model describes the joint risk of event according to the latent classes and two specifications of the risk function are considered: a parametric function and a semi-parametric function based on splines. Depending on the chosen risk function, estimation is performed by a maximum likelihood or a maximum penalized likelihood approach. A simulation study validates the estimation procedure. As a latent class model relies on the strong assumption that the markers and the time-to-event are independent conditionally on the latent classes, a test of conditional independence is proposed using the residuals conditional on time-to-event. The procedure does not require any posterior classification and can be conducted using standard statistical softwares. The methodology is applied to describe profiles of cognitive decline in the elderly and their associated risk of dementia.     

Variants of the general interval power function

The article gives an overview of power function variants and compares three differently extensive versions for use in interval arithmetics. Aiming at the general power function for inclusion in interval libraries, which is defined for as many pairs of base and exponent as possible, we observe that the definition of a power for each such pair depends on the context. This problem eventually comes up at the point where reasonable doubts about the definition $0^0$ and powers with negative base in correlation with a non-integral exponent arise. We come up with several variants serving distinct purposes, yet also recommend a general-purpose power function, which is unique for being restricted to integral exponents on the domain of negative bases. Three different variants of interval power functions satisfy all meaningful general exponentiation needs. We provide a unified treatment to handle the variants and present valuable implementation techniques for the computation of these interval functions along with a mathematic foundation.     

To the optimal identification of multivariate systems under perturbations of unknown covariances

We consider the problem of parameter and covariance estimation for multivariate stochastic systems described by regression models with special structure perturbations of unknown covariance. Sufficient conditions of uniformly optimal estimations are obtained for system parameters and covariances. The observation vector distribution family is factorized, and the full sufficient statistics is found under those conditions. Equations for uniformely optimal unbiased estimates of covariance parameters are obtained.     

Analytic and bootstrap approximations of prediction errors under a multivariate Fay-Herriot model

The prediction of vectors of small area quantities based on a multivariate Fay-Herriot model is addressed. For this, an empirical best linear unbiased predictor (EBLUP) of the target vector is used, where the model parameters are estimated by two different methods based on moments. The mean cross product error matrix of the multidimensional EBLUP is approximated both analytically and by a wild bootstrap method that yields direct and bias-corrected bootstrap estimators. A simulation study compares the small sample properties of the bootstrap estimators and the analytical approximation, including a comparison under lack of normality. Finally, the number of replicates needed for the bootstrap procedures to get stabilized are studied.     

MULCOX2: a general computer program for the Cox regression analysis of multivariate failure time data

Multivariate failure time data is commonly encountered in biomedicine, because each study subject may experience multiple events or because there exists clustering of subjects such that failure times within the same cluster are correlated. MULCOX2 implements a general statistical methodology for analyzing such data. This approach formulates the marginal distributions of multivariate failure times by Cox proportional hazards models without specifying the nature of dependence among related failure times. The baseline hazard functions for the marginal models may be identical or different. A variety of statistical inference can be made regarding the effects of (possibly time-dependent) covariates on the failure rates. Although designed primarily for the marginal approach, MULCOX2 is general enough to implement several alternative methods. The program runs on any computer with a FORTRAN compiler. The running time is minimal. Two illustrative examples are provided.     

Interpretable tourism volume forecasting with multivariate time series under the impact of COVID-19

Neural Computing and Applications - This study proposes a novel interpretable framework to forecast the daily tourism volume of Jiuzhaigou Valley, Huangshan Mountain, and Siguniang Mountain in...     

Joint estimation of mean-covariance model for longitudinal data with basis function approximations

When the selected parametric model for the covariance structure is far from the true one, the corresponding covariance estimator could have considerable bias. To balance the variability and bias of the covariance estimator, we employ a nonparametric method. In addition, as different mean structures may lead to different estimators of the covariance matrix, we choose a semiparametric model for the mean so as to provide a stable estimate of the covariance matrix. Based on the modified Cholesky decomposition of the covariance matrix, we construct the joint mean-covariance model by modeling the smooth functions using the spline method and estimate the associated parameters using the maximum likelihood approach. A simulation study and a real data analysis are conducted to illustrate the proposed approach and demonstrate the flexibility of the suggested model.     

Conquering inseparability: Primary decomposition and multivariate factorization over algebraic function fields of positive characteristic

Algebraic function fields of positive characteristic are non-perfect fields, and many standard algorithms for solving some fundamental problems in commutative algebra simply do not work over these fields. This paper presents practical algorithms for the first time for (1) computing the primary decomposition of ideals of polynomial rings defined over such fields and (2) factoring arbitrary multivariate polynomials over such fields. Difficulties involving inseparability and the situation where the transcendence degree is greater than one are completely overcome, while the algorithms avoid explicit construction of any extension of the input base field. As a corollary, the problem of computing the primary decomposition of a positive-dimensional ideal over a finite field is also solved. The algorithms perform very effectively in an implementation within the Magma Computer Algebra System, and an analysis of their practical performance is given.     

A power function model for determining sample sizes for the operations of multivariate control charts

Using the hypothesis-testing approach, we develop a model for determining sample sizes for the operation of multivariate control charts. A simple solution procedure that can be processed on any personal or small computer is also developed. The effect of correlation between pairs of variables on the performance of the model is studied. The performances of multivariate and univariate control charts are compared under the model. Before the development of the model, a brief review of multivariate test of hypothesis and multivariate control charts was done. The model is recommended for any quality control engineer who may like to specify a desired level of protection against inferior quality.     

Explicit exact analysis of infinite periodic structures under general loading

This paper deals with the explicit analysis of infinite periodic structures under arbitrary loadings. In the context or structural stiffness optimization, with its inherent problem of multiple reanalysis, the purpose is to obtain expressions for the stress resultants anywhere in the infinite structure as an explicit function of the stiffnesses of the elements. Following the method of the representative cell the analysis of an infinite structures is reduced to the analysis of single module under transformed loading and boundary conditions by using the discrete Fourier transform. This produces the equilibrium, strain-displacements and constitutive equations in terms of complex-valued displacements, generalized strains and generalized stresses transforms. Next an existing formula is used to write the stress resultants transforms explicitly in terms of the stiffnesses. Finally one computes the stress resultants wherever needed in the real structure by means of the inverse Fourier transform. The exact formula for the stress resultants is usually impractical due to the large number of terms involved in the analytical expressions. What makes the approach practical herein is the very reduced size of the repeating module that is to be analysed, which renders the analytical formula more tractable in many cases. The technique is illustrated with the explicit analysis of an infinite truss with 1D translational symmetry and of an infinite grid of orthogonal beams on elastic supports with 2D translational symmetry. Received December 4, 2000     

A sensitivity analysis of solving joint replenishment problems using the RAND method under inaccurate holding cost estimates and demand forecasts

This paper presents a study of solving the joint replenishment problem (JRP) by using the RAND method, a heuristic approach that has been proven to find almost as good as optimal solutions, under uncertain customer demands and inaccurate unit holding cost estimation. The classical JRP deals with the issue of determining a replenishment policy that minimizes the total cost of replenishing multiple products from a single supplier. The total cost considered in the JRP consists of a major ordering cost independent of the number of items in the order, a minor ordering cost depending on the items in the order, and the holding cost. There have been many heuristic approaches proposed for solving the JRP. Most of the research work was done under the assumptions that the demand for each item type and the unit holding cost are known and constant. However, in the real world accurately forecasting customer demands and precisely estimating the unit holding cost are both difficult. Besides, the real values of the demands and the unit holding cost may change over the replenishment horizon. The present study addresses the issue of the uncertain demands and the unit holding cost to the JRP and investigates how misestimates of these demands and holding costs may influence the replenishment policy as determined by the famous JRP heuristic, the RAND method.     

A unified approach to optimization of structural members under general constraints

A unified numerical approach, based on a control parameterization technique, for solving structural crosssectional optimization problems is presented. The key factor to the unified formulation lies in the framing of the objective functional and the constraints into the same unified canonical form. Consequently, the different types of objective functionals, geometrical and performance constraints can be treated in the same way, thus paving the path for the problems to be solved under a single approach using a general purpose software. To demonstrate this versatile approach, several illustrative examples of cross-sectional shape optimization of structural members under a variety of constraints were examined.