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Modelling and forecasting interval-valued time series (ITS) have received increasing attention in statistics and econometrics. An interval-valued observation contains more information than a point-valued observation in the same time period. The previous literature has mainly considered modelling and forecasting a univariate ITS. However, few works attempt to model a vector process of ITS. In this paper, we propose an interval-valued vector autoregressive moving average (IVARMA) model to capture the cross-dependence dynamics within an ITS vector system. A minimum-distance estimation method is developed to estimate the parameters of an IVARMA model, and consistency, asymptotic normality and asymptotic efficiency of the proposed estimator are established. A two-stage minimum-distance estimator is shown to be asymptotically most efficient among the class of minimum-distance estimators. Simulation studies show that the two-stage estimator indeed outperforms other minimum-distance estimators for various data-generating processes considered.

The purpose of this paper is to propose an efficient space-time operator-splitting method for the high-dimensional vector-valued Allen–Cahn (AC) equations. The key of the space-time operator-splitting is to devide the complex partial differential equations into simple heat equations and nolinear ordinary differential equations.

Each component of high-dimensional heat equations is split into a series of one-dimensional heat equations in different spatial directions. The nonlinear ordinary differential equations are solved by a stabilized semi-implicit scheme to preserve the upper bound of the solution. The algorithm greatly reduces the computational complexity and storage requirement.

The theoretical analyses of stability in terms of upper bound preservation and mass conservation are shown. The numerical results of phase separation, evolution of the total free energy and total mass conservation show the effectiveness and accuracy of the space-time operator-splitting method.

Extensive 2D/3D numerical tests demonstrated the efficacy and accuracy of the proposed method.

The space-time operator-splitting method reduces the complexity of the problem and reduces the storage space by turning the high-dimensional problem into a series of 1D problems. We give the theoretical analyses of upper bound preservation and mass conservation for the proposed method.

The performance of Aoki’s state space algorithm and the Cartesian ARIMA search algorithm (CARlMA) of Östermark and Höglund is compared. The analysis is carried out on a set of stock prices on the Helsinki (Finland) and Stockholm (Sweden) Stock Exchanges. Demonstrates that the Finnish and Swedish stock markets differ in predictability of stock prices. With Finnish stock data, Aoki’s state space algorithm outperforms the subset of MAPE minimizing forecasts. In contrast, with Swedish stock data, ARIMA‐models of a fairly simple structure outperform Aoki’s algorithm. The stock markets are seen to differ in complexity of time series models as well as in predictability of individual asset prices.

To demonstrate the scalability of the genetic hybrid algorithm (GHA) in monitoring a local neural network algorithm for difficult non‐linear/chaotic time series problems.

GHA is a general‐purpose algorithm, spanning several areas of mathematical problem solving. If needed, GHA invokes an accelerator function at key stages of the solution process, providing it with the current population of solution vectors in the argument list of the function. The user has control over the computational stage (generation of a new population, crossover, mutation etc) and can modify the population of solution vectors, e.g. by invoking special purpose algorithms through the accelerator channel. If needed, the steps of GHA can be partly or completely superseded by the special purpose mathematical/artificial intelligence‐based algorithm. The system can be used as a package for classical mathematical programming with the genetic sub‐block deactivated. On the other hand, the algorithm can be turned into a machinery for stochastic analysis (e.g. for Monte Carlo simulation, time series modelling or neural networks), where the mathematical programming and genetic computing facilities are deactivated or appropropriately adjusted. Finally, pure evolutionary computation may be activated for studying genetic phenomena. GHA contains a flexible generic multi‐computer framework based on MPI, allowing implementations of a wide range of parallel models.

The results indicate that GHA is scalable, yet due to the inherent stochasticity of neural networks and the genetic algorithm, the scalability evidence put forth in this paper is only indicative. The scalability of GHA follows from maximal node intelligence allowing minimal internodal communication in problems with independent computational blocks.

The paper shows that GHA can be effectively run on both sequential and parallel platforms. The multicomputer layout is based on maximizing the intelligence of the nodes – all nodes are provided with the same program and the available computational support libraries – and minimizing internodal communication, hence GHA does not limit the size of the mesh in problems with independent computational tasks.

The purpose of this paper is to study the effects of hedging with options and cardinality constraints in multi‐period portfolio management systems.

The paper focuses on a recursive multi‐period portfolio management formulation (SHAREX) subject to hedging with cardinality constraints and options. The problem formulation is tested with observed and simulated data.

The yield of the multi‐period cardinality constrained option hedging framework under integer‐valued transactions and fixed and variable transactions costs exceeds the riskless return predicted by the Black‐Scholes model in equilibrium.

The paper demonstrates that the multiple representations framework constructed to generate optimal predictions provides accurate forecasts with obvious value for portfolio management.

Considers the modelling of dynamic systems using biased regression and spectral methods. Provides evidence on the power of transfer function modelling for unravelling the empirical connection between endogenous and exogenous (control) variables in both regression type and spectral input‐output systems. The Multiple Input Transfer Function Noise Model – of specific value when the input variables are collinear – has previously been used to demonstrate the connection between macroeconomic forces and stock market pricing on a thin security market. Compares the adequacy of representative time and frequency domain algorithms for modelling observed data series. The estimations are done with the combined Transfer Function and Cartesian ARIMA Search algorithm of Östermark and Höglund and the CAPM/APM programs of Östermark.

The axisymmetric steady‐state convective‐diffusive thermal field problem associated with direct‐chill, semi‐continuously cast billets has been solved using the dual reciprocity boundary element method. The solution is based on a formulation which incorporates the one‐phase physical model, Laplace equation fundamental solution weighting, and scaled augmented thin plate splines for transforming the domain integrals into a finite series of boundary integrals. Realistic non‐linear boundary conditions and temperature variation of all material properties are included. The solution is verified by comparison with the results of the classical finite volume method. Results for a 0.500[m] diameter Al 4.5 per cent Cu alloy billet at typical casting conditions are given.

To solve the multi‐period portfolio management problem under transactions costs.

We apply a recently designed super genetic hybrid algorithm (SuperGHA) – an integrated optimisation system for simultaneous parametric search and non‐linear optimisation – to a recursive portfolio management decision support system (SHAREX). The parametric search machine is implemented as a genetic superstructure, producing tentative parameter vectors that control the ultimate optimisation process.

SHAREX seems to outperform the buy and hold‐strategy on the Finnish stock market. The potential of a technical portfolio system is best exploitable under favorable market conditions.

A number of robust engines for matrix algebra, mathematical programming and numerical calculus have been integrated with SuperGHA. The engines expand its scope as a general‐purpose algorithm for mathematical programming.

This paper gives a selective review on some recent developments of nonparametric methods in both continuous and discrete time finance, particularly in the areas of nonparametric estimation and testing of diffusion processes, nonparametric testing of parametric diffusion models, nonparametric pricing of derivatives, nonparametric estimation and hypothesis testing for nonlinear pricing kernel, and nonparametric predictability of asset returns. For each financial context, the paper discusses the suitable statistical concepts, models, and modeling procedures, as well as some of their applications to financial data. Their relative strengths and weaknesses are discussed. Much theoretical and empirical research is needed in this area, and more importantly, the paper points to several aspects that deserve further investigation.

This study aims to derive a novel spatial numerical method based on multidimensional local Taylor series representations for solving high-order advection-diffusion (AD) equations.

The parabolic AD equations are reduced to the nonhomogeneous elliptic system of partial differential equations by utilizing the Chebyshev spectral collocation method (ChSCM) in the temporal variable. The implicit-explicit local differential transform method (IELDTM) is constructed over two- and three-dimensional meshes using continuity equations of the neighbor representations with either explicit or implicit forms in related directions. The IELDTM yields an overdetermined or underdetermined system of algebraic equations solved in the least square sense.

The IELDTM has proven to have excellent convergence properties by experimentally illustrating both h-refinement and p-refinement outcomes. A distinctive feature of the IELDTM over the existing numerical techniques is optimizing the local spatial degrees of freedom. It has been proven that the IELDTM provides more accurate results with far fewer degrees of freedom than the finite difference, finite element and spectral methods.

This study shows the derivation, applicability and performance of the IELDTM for solving 2D and 3D advection-diffusion equations. It has been demonstrated that the IELDTM can be a competitive numerical method for addressing high-space dimensional-parabolic partial differential equations (PDEs) arising in various fields of science and engineering. The novel ChSCM-IELDTM hybridization has been proven to have distinct advantages, such as continuous utilization of time integration and optimized formulation of spatial approximations. Furthermore, the novel ChSCM-IELDTM hybridization can be adapted to address various other types of PDEs by modifying the theoretical derivation accordingly.