Identification of the Interactions of Industry-dependent State Variables on Movement of National Market Index

摘要

This work is a self-contained exposition of a cybernetical approach to develop mathematical model of national market index incorporating the parameters of discrete event industry-dependent state variable. The development of the process leads to an appealing environment with the behavioural equations and latent variables as the important supporting characters. The framework presented incorporates problems of representations, questions of parameterisation and procedure for identification algorithm for obtaining models for observed data. The concept of dynamical systems are elaborated in the present dissertation and it leads to the development of dynamical systems where phsyical state variables interact in accordance with optically designed decision algorithm. We shall focus on dynamical systems which are quite amenable to mathematical models of linear or non-linear types. The exposition deals with an application of the cybernetical method to develop polynomials of optimum complexity with multilayer group method of data handling algorithm of technical cybernetics through an observation-conjecure-modelling-validation cycle. One of the goals of technical cybernetics has been to capture the major elements of a dynamical process under the umbrella of a formal mathematical synthesis. The work presented here formalises a specific dynamic situation, namely the construction of a finite dimensional process for daily movement of national market index. It has been clearly demonstrated with observed data that the flexibility of the algorithms is remarkably broad. Indeed, it is possible to chosse free parameters in such a way that the entire formal modelling process can be interpreted as a loop shaping problem, where the loops are the layers in the multilayer selection procoess, and the loop-breaking takes place at the optimum layer through a certain specific choice of parameters.