Estimation of market efficiency process within time-varying autoregressive models by extended Kalman filtering approach

This paper explores a time-varying version of weak-form market efficiency that is a key component of the so-called Adaptive Market Hypothesis (AMH). One of the most common methodologies used for modeling and estimating a degree of market efficiency lies in an analysis of the serial autocorrelation in observed return series. Under the AMH, a time-varying market efficiency level is modeled by time-varying autoregressive (AR) process and traditionally estimated by the Kalman filter (KF). Being a linear estimator, the KF is hardly capable to track the hidden nonlinear dynamics that is an essential feature of the models under investigation. The contribution of this paper is threefold. We first provide a brief overview of time-varying AR models and estimation methods utilized for testing a weak-form market efficiency in econometrics literature. Secondly, we propose novel accurate estimation approach for recovering the hidden process of evolving market efficiency level by the extended Kalman filter (EKF). Thirdly, our empirical study concerns an examination of the Standard and Poor's 500 Composite stock index and the Dow Jones Industrial Average index. Monthly data covers the period from November 1927 to June 2020, which includes the U.S. Great Depression, the 2008-2009 global financial crisis and the first wave of recent COVID-19 recession. The results reveal that the U.S. market was affected during all these periods, but generally remained weak-form efficient since the mid of 1946 as detected by the estimator

Continuous-discrete unscented Kalman filtering framework by MATLAB ODE solvers and square-root methods

This paper addresses the problem of designing the {\it continuous-discrete} unscented Kalman filter (UKF) implementation methods. More precisely, the aim is to propose the MATLAB-based UKF algorithms for {\it accurate} and {\it robust} state estimation of stochastic dynamic systems. The accuracy of the {\it continuous-discrete} nonlinear filters heavily depends on how the implementation method manages the discretization error arisen at the filter prediction step. We suggest the elegant and accurate implementation framework for tracking the hidden states by utilizing the MATLAB built-in numerical integration schemes developed for solving ordinary differential equations (ODEs). The accuracy is boosted by the discretization error control involved in all MATLAB ODE solvers. This keeps the discretization error below the tolerance value provided by users, automatically. Meanwhile, the robustness of the UKF filtering methods is examined in terms of the stability to roundoff. In contrast to the pseudo-square-root UKF implementations established in engineering literature, which are based on the one-rank Cholesky updates, we derive the stable square-root methods by utilizing the $J$-orthogonal transformations for calculating the Cholesky square-root factors

MATLAB-based general approach for square-root extended-unscented and fifth-degree cubature Kalman filtering methods

A stable square-root approach has been recently proposed for the unscented Kalman filter (UKF) and fifth-degree cubature Kalman filter (5D-CKF) as well as for the mixed-type methods consisting of the extended Kalman filter (EKF) time update and the UKF/5D-CKF measurement update steps. The mixed-type estimators provide a good balance in trading between estimation accuracy and computational demand because of the EKF moment differential equations involved. The key benefit is a consolidation of reliable state mean and error covariance propagation by using delicate discretization error control while solving the EKF moment differential equations and an accurate measurement update according to the advanced UKF and/or 5D-CKF filtering strategies. Meanwhile the drawback of the previously proposed estimators is an utilization of sophisticated numerical integration scheme with the built-in discretization error control that is, in fact, a complicated and computationally costly tool. In contrast, we design here the mixed-type methods that keep the same estimation quality but reduce a computational time significantly. The novel estimators elegantly utilize any MATLAB-based numerical integration scheme developed for solving ordinary differential equations (ODEs) with the required accuracy tolerance pre-defined by users. In summary, a simplicity of the suggested estimators, their numerical robustness with respect to roundoff due to the square-root form utilized as well as their estimation accuracy due to the MATLAB ODEs solvers with discretization error control involved are the attractive features of the novel estimators. The numerical experiments are provided for illustrating a performance of the suggested methods in comparison with the existing ones

Square-root filtering via covariance SVD factors in the accurate continuous-discrete extended-cubature Kalman filter

This paper continues our research devoted to an accurate nonlinear Bayesian filters' design. Our solution implies numerical methods for solving ordinary differential equations (ODE) when propagating the mean and error covariance of the dynamic state. The key idea is that an accurate implementation strategy implies the methods with a discretization error control involved. This means that the filters' moment differential equations are to be solved accurately, i.e. with negligible error. In this paper, we explore the continuous-discrete extended-cubature Kalman filter that is a hybrid method between Extended and Cubature Kalman filters (CKF). Motivated by recent results obtained for the continuous-discrete CKF in Bayesian filtering realm, we propose the numerically stable (to roundoff) square-root approach within a singular value decomposition (SVD) for the hybrid filter. The new method is extensively tested on a few application examples including stiff systems

Multi-layered plate finite element models with node-dependent kinematics for smart structures with piezoelectric components

Abstract This article presents a type of plate Finite Element (FE) models with adaptive mathematical refinement capabilities for modeling laminated smart structures with piezoelectric layers or distributed patches. The p-version shape functions are used in combination with the higher-order Layer-Wise (LW) kinematics adopting hierarchical Legendre polynomials. Node-Dependent Kinematics (NDK) is employed to implement local LW models in the regions with piezoelectric components and simulate the global substrate structure with the Equivalent Single-Layer (ESL) approach. Through the proposed NDK FE models, the electro-mechanical behavior of smart structures can be predicted with high fidelity and numerical efficiency, and various patch configurations can be conveniently modeled through one set of mesh grids. Moreover, the effectiveness and efficiency of the NDK FE approach are assessed through numerical examples and its application is demonstrated

Evaluation of shear and membrane locking in refined hierarchical shell finite elements for laminated structures

oai:zenodo.org:50662Abstract Shear and membrane locking phenomena are fundamental issues of shell finite element models. A family of refined shell elements for laminated structures has been developed in the framework of Carrera Unified Formulation, including hierarchical elements based on higher-order Legendre polynomial expansions. These hierarchical elements were reported to be relatively less prone to locking phenomena, yet an exhaustive evaluation of them regarding the mitigation of shear and membrane locking on laminated shells is still essential. In the present article, numerically efficient integration schemes for hierarchical elements, including also reduced and selective integration procedures, are discussed and evaluated through single-element p-version finite element models. Both shear and membrane locking are assessed quantitatively through the estimation of strain energy components. The numerical results show that the fully integrated hierarchical shell elements can overcome the shear and membrane locking effectively when a sufficiently high polynomial degree is reached. Reduced and selective integration schemes can help with the mitigation of locking on lower-order hierarchical shell elements

Assessment of the possibility for large-scale 238Pu production in a VVER-1000 power reactor

The paper presents the estimates for the possibility for large-scale production of 238Pu in the core of a VVER-1000 power reactor. The Np-fraction of minor actinides extracted from transuranic radioactive waste is proposed to be used as the starting material. The irradiation device with NpO2 fuel elements is installed at the reactor core center. The NpO2 fuel lattice pitch is varied and the irradiation device is surrounded by a heavy moderator layer to create the best possible spectral conditions for large-scale production (~ 3 kg/year) of conditioned plutonium with the required isotopic composition (not less than 85% of 238Pu and not more than 2 ppm of 236Pu). Plutonium with such isotopic composition can be used as the thermal source in thermoelectric radioisotope generators and in cardiac pacemakers. It has been demonstrated that the estimated scale of the 238Pu production in a VVER-type power reactor exceeds considerably the existing scale of its production in research reactors

ПРОГНОЗ ЗЕМЛЕТРЯСЕНИЙ ПО ДАННЫМ МОНИТОРИНГА ГИДРОГЕОДЕФОРМАЦИОННОГО ПОЛЯ

The paper discusses further ways to improve the geodynamic informativity of the hydrogeodeformation field (HGD field) monitoring. New methods for efficient assessment of the stressstrain state of the geological environment and seismic hazard are proposed. There are described the methods of monitoring data processing, distinguishing of HGD cycles, and construction of «forecasting» contours along extremums of these cycles. It is revealed that responses of the HGD field to development of planetaryscale endogenic geodynamic processes of earthquake preparation (with M>7) are simultaneously manifested in all seismically active regions of Russia which are remote from each other. Such responses occur from one to three months prior to such seismic events. The mechanism of this phenomenon can be disputed. The authors support the «planetary pulsation» concept which is up for the most recent debates. As evidenced by the HGD field monitoring data, strong earthquakes are a consequence of this phenomenon.Рассмотрены пути дальнейшего повышения геодинамической информативности мониторинга гидрогеодеформационного (ГГД) поля, разработаны новые методы оперативной оценки напряженно-деформированного состояния геологической среды и сейсмической опасности. В статье изложены способы обработки данных мониторинга, выделения ГГД циклов и проведения «прогнозных» линий по экстремумам этих циклов. Обнаружена одновременная реакция ГГД поля во всех сейсмоактивных регионах России, значительно удаленных друг от друга, на развитие планетарных эндогенных геодинамических процессов подготовки сильных землетрясений (магнитудой более 7) за 1–3 месяца до их проявления. Механизм этого обнаруженного явления вызывает дискуссии. Авторы в этом вопросе склонны придерживаться обсуждаемой в последнее время гипотезы «планетарной пульсации». Следствие такого явления, как показывают результаты мониторинга ГГД поля, – сильные землетрясения

КОМПЛЕКСНАЯ МОДЕЛЬ ОРГАНИЗАЦИИ АВТОМАТИЗИРОВАННОГО ПРОЦЕССНОГО УПРАВЛЕНИЯ ЖИЗНЕННЫМ ЦИКЛОМ ПОДГОТОВКИ СПЕЦИАЛИСТОВ НА ОСНОВЕ СТРУКТУРИРОВАНИЯ КОНТЕНТА ВУЗА И ПРЕДПРИЯТИЯ

This article discusses the modern point of view, the issue of developing methods of forming the structure of the process lifecycle management of specialisttraining in conjunction with the University of industrial enterprise on the basisof a comprehensive content base chair. The possibility of using IT to improve the efficiency of educational processes.В данной статье рассматривается с современной точки зрения вопрос разработки методики формирования структуры системы процессного управления жизненным циклом подготовки специалистов университетом совместно с промышленным предприятием на основе комплексного контентабазовойкафедры. РассматриваетсявозможностьпримененияИТдля повышения эффективности образовательных процессов