Modeling and Forecasting Financial Heteroscedastic Processes

Abstract

Context: Nowadays in the field of economics, ecology, demographics, we observed nonlinear non-stationary processes. To evaluate the models and forecasts of the processes under consideration, it is necessary to develop special methods. Modeling methodologies include potential uncertainties that arise during data filtering and processing, as well as model structures and parameter estimates.Objective: To develop a modified methodology for constructing mathematical models of nonlinear non-stationary processes that will help to achieve high-quality forecasts. The analyzed heteroskedastic processes create a wide class of nonlinear non-stationary processes and are considered in many areas of research.Methods: To achieve the main goal of the work, a systematic approach is used to build models and forecasts. Used modified methodologies for modeling non-linear non-stationary processes and methods for identifying and accounting for all uncertainties. To account for uncertainties, used methods to refine the order of the model with an adaptive approach to modeling and automatically search for the most optimal structure using complex statistical criteria. A description of non-linearities is also performed using alternative analytical forms with the ability to perform a subsequent assessment of the predictions received.Results: The work proposed modified modeling methods, built new models and forecasts. As a result of experiments, it was an achievement that nonlinear models and forecasts with using filtering (exponential, elliptical, Kalman filtering) provide a possibility for computing high-quality results and hight quality indicators for the process under study and their variance.Conclusions: The application of the proposed modeling methodology allows you to simulate the structure and parameters of the model, which are built on the basis of statistical data. The resulting models show high accuracy and good quality for short-term forecasts.