71 research outputs found
Local Lagged Adapted Generalized Method of Moments: An Innovative Estimation and Forecasting Approach and its Applications.
In this work, an attempt is made to apply the Local Lagged Adapted Generalized Method of Moments (LLGMM) to estimate state and parameters in stochastic differential dynamic models. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, energy commodity markets, financial, medical, military, physical sciences and social sciences. The byproducts of this innovative approach (LLGMM) are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). Moreover, LLGMM is a dynamic non-parametric method. The DTIDMLSMVSP is an alternative approach to the GARCH (1,1) model, and it provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equations. Furthermore, applications of LLGMM to energy commodities price, U.S. Treasury Bill interest rate and the U.S.–U.K. foreign exchange rate data strongly exhibit its unique role, scope and performance, in particular, in forecasting and confidence-interval problems in applied statistics
Local Lagged Adapted Generalized Method Of Moments And Applications
In this work, an attempt is made for developing the local lagged adapted generalized method of moments (LLGMM). This proposed method is composed of: (1) development of the stochastic model for continuous-time dynamic process, (2) development of the discrete-time interconnected dynamic model for statistic process, (3) utilization of Euler-type discretized scheme for nonlinear and non-stationary system of stochastic differential equations, (4) development of generalized method of moment/observation equations by employing lagged adaptive expectation process, (5) introduction of the conceptual and computational parameter estimation problem, (6) formulation of the conceptual and computational state estimation scheme and (7) definition of the conditional mean square Є -best sub optimal procedure. The development of LLGMM is motivated by parameter and state estimation problems in continuous-time nonlinear and non-stationary stochastic dynamic model validation problems in biological, chemical, engineering, financial, medical, physical and social sciences. The byproducts of LLGMM are the balance between model specification and model prescription of continuous-time dynamic process and the development of discrete-time interconnected dynamic model of local sample mean and variance statistic process (DTIDMLSMVSP). DTIDMLSMVSP is the generalization of statistic (sample mean and variance) drawn from the static dynamic population problems. Moreover, it is also an alternative approach to the GARCH (1,1) model and its many related variant models (e.g., EGARCH model, GJR GARCH model). It provides an iterative scheme for updating statistic coefficients in a system of generalized method of moment/observation equation. Furthermore, application of the LLGMM method to stochastic differential dynamic models for energy commodity price, U. S. Treasury Bill Yield Interest Rate and U. S.-U.K. Foreign Exchange Rate exhibits its unique role and scope
Global Analysis of a Stochastic Two-Scale Network Human Epidemic Dynamic Model with Varying Immunity Period
A stochastic SIR epidemic dynamic model with distributed-time-delay, for a two-scale dynamic population is derived. The distributed time delay is the varying naturally acquired immunity period of the removal class of individuals who have recovered from the infection, and have acquired natural immunity to the disease. We investigate the stochastic asymptotic stability of the disease free equilibrium of the epidemic dynamic model, and verify the impact on the eradication of the disease
Large-scale stochastic hereditary systems under Markovian structural perturbations. Part II. Qualitative analysis of isolated subsystems
In this part of the work, the convergence and stability analysis
of isolated subsystems of stochastic hereditary systems under
random structural perturbations is investigated. The variational
comparison theorems developed in Part I are used to achieve this
goal. Under algebraic conditions on the rate coefficients,
time-delay, and an intensity matrix associated with the Markov
chain, convergence and stability results are obtained.
Furthermore, it is shown that these properties are affected by
hereditary and random structural perturbations effects. It is
further shown that the mathematical conditions are algebraically
simple and are robust to the parametric changes. This
investigation provides a basis for drawing the conclusions about
the overall large-scale system
Large-scale stochastic hereditary systems under Markovian structural perturbations. Part I. Variational comparison theorems
This three-part series work investigates the qualitative analysis of large-scale stochastic hereditary systems under random structural perturbations. The random structural perturbations are described by a Markov chain with a finite number of states. The first part of this three-part series work deals with the problem formulation and the development of mathematical tool to undertake this investigation. In this first part, we present variational comparison theorems for isolated subsystems of large-scale stochastic hereditary systems under Markovian structural perturbations. This part lays down the basis for the study of hierarchic systems
Large-scale stochastic hereditary systems under Markovian structural perturbations. Part III. Qualitative analysis
In this final part of the work, the convergence and stability
analysis of large-scale stochastic hereditary systems under random
structural perturbations is investigated. This is achieved
through the development and the utilization of comparison theorems
in the context of vector Lyapunov-like functions and
decomposition-aggregation method. The byproduct of the
investigation suggests that the qualitative properties of
decoupled stochastic hereditary subsystems under random structural
perturbations are preserved, as long as the self-inhibitory
effects of subsystems are larger than cross-interaction effects of
the subsystems. Again, it is shown that these properties are
affected by hereditary and random structural perturbations
effects. It is further shown that the mathematical conditions are
algebraically simple, and are robust to the parametric changes.
Moreover, the work generates a concept of block quasimonotone
nondecreasing property that is useful for the investigation of
hierarchic systems. These results are further extended to the
integrodifferential equations of Fredholm type
Local lagged adapted generalized method of moments dynamic process
Aspects of a local lagged adapted generalized method of moments (LLGMM) dynamic process are described herein. In one embodiment, the LLGMM process includes obtaining a discrete time data set as past state information of a continuous time dynamic process over a time interval, developing a stochastic model of the continuous time dynamic process, generating a discrete time interconnected dynamic model of local sample mean and variance statistic processes (DTIDMLSMVSP) based on the stochastic model, and calculating a plurality of admissible parameter estimates for the stochastic model using the DTIDMLSMVSP. Further, in some embodiments, the process further includes, for at least one of the plurality of admissible parameter estimates, calculating a state value of the stochastic model to gather a plurality of state values, and determining an optimal admissible parameter estimate among the plurality of admissible parameter estimates that results in a minimum error among the plurality of state values
Multi-Cultural Dynamics on Social Networks under External Random Perturbations
This work deals with the development of multi-cultural network-centric dynamic models under the influence of personal intra- and inter-members, as well as community. Each individual member of a society is influenced by her/his interactions with fellow members of the family, neighborhood, region and the universe. The behavior of such complex and highly interacting social networks is characterized by stochastic interconnected dynamical systems. The primary goal is on laying down an investigation of both qualitative and quantitative properties of this network dynamical system. In particular, we would like to determine the regions of conflicts and coexietence as well as to establish the cohesion and stability of emerging states. This is achieved by employing the method of system of differential inequalities and comparison theorems in the context of the energy function. The developed energy function method provides estimates for regions of conflict and cooperation. Moreover, the method also provides sufficient conditions for the community cohesion and stability in a systematic way
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