The development of the method of modelling and forecasting of nonlinear heteroscedastic processe

DOI №______

Abstract

The article is dedicated to the analysis of methods of estimation of the parameters of nonlinear stochastic models of volatility using Monte Carlo method for mark chains on the basis of Gibs algorithms and its modifications in the form of procedure of adaptive sortings out. In order to smooth the line of outcome data and the sequence of parameters estimation calculated with the help of iteration algorithms, the corresponding modifications of Kalman filter are used. The results of estimation of the parameters of stochastic model volatility on the basis of the fact data used, are presented. To conduct the computing experiments, the procedures of system OpenBUGS have been used and special programme providing on Java language has been developed. In economy, finance, some technic and technological systems, nonstationary processes with time-changed dispersion are wide spread, they are called heteroscedastic. Thus, heteroscedastic are the processes with time-changed dispersion, homocodic are the processes with static dispersion on a certain time period which are described in the process of modelling and forecasting.
Heteroscedastic processes are a part of a wide range of nonstationary processes that include such processes as processes with determinated and stochastic trends, processes with changed dispersion, processes which are characterized by time-changed mathematical expectation and changed dispersion simultaneously, processes with changed covariation. As far as the development of nonstationary processes is represented by time lines, in order to increase the quality of forecasting of random trends and volatility by developing new models and methods of their estimation, the main attention in this work is dedicated to the problems of modelling and forecasting of fact time lines in combination with the use of methology of hybrid adaptive immune algorithms and polynomial neural networks. Such models are successfully used in the decision making support systems to forecast the cost of actions and other stock actives, exchange rates, levels of inflation etc.

Keywords: nonlinear heteroscedastic methods, Monte Carlo method, Gibbs algorithm, Kalman filter, modelling, decision making support systems.

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