Modeling of nonlinear for nonstacionary processes

DOI №______

Abstract

A new robust Kalman filter (KF) algorithm was developed for estimating the states of nonlinear nonstationary time series and smoothing volatility estimates. Also analytic procedure was elaborated for analyzing convergence of the estimates produced by the robust filter. The parametric synthesis of Kalman filter using evolutionary computational schemes and reinforced learning was proposed for forecasting nonstationary time series that is distinguished with high quality of short-term volatility forecasts. The procedure is different acceptable by volume and complexity of computational cost, high quality assessments of the states of nonstationary processes Application of Kalman filter in the frames of adaptive modeling and forecasting system (AMFS) also turned out to be useful from the following points of view: (1) KF provides a possibility for taking explicitly into consideration covariance of random external disturbance for the process under study as well as measurement noise; (2) optimal filtering algorithms allow to hire a rather wide spectrum of (linear and nonlinear) models in the form of differential and difference equations after their transformation into state space form; (3) in the process of its execution optimal filter automatically generates one-step ahead prediction that could be used further on for decision making; (4) multi-step ahead prediction is also possible; (5) KF allows to estimate (and predict) non-measurable (hidden) variables using measurements of other (related) variables; (6) adaptive forms of KF allow for model parameter adaptation including the covariance mentioned.
The further efforts regarding improvement of short- and middle-term forecasting will be directed towards constructing of new forecasts combination schemes using appropriately optimized weights for correctly selected techniques in the frames of decision support system. It is also important to hire ideologically different techniques for combination of the forecasts. For example, regressive techniques will be supplemented with probabilistic approaches.

Keywords: nonlinear nonstationary processes; optimal estimation; Kalman filter; mathematical modelling.

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