UDC 336.144.36, 519.216.3, 519.254
A GENERALIZATION OF THE ARIMA MODEL TO THE NONLINEAR
AND CONTINUOUS CASES
Abstract. A method of extending the classical ARIMA and GARCH models to the continuous and nonlinear cases is considered. Stochastic functional differential equations, which are a natural generalization of the sums of independent random variables, are considered extended models. Along with the new model, a relevant optimization problem for estimating model parameters is considered, and the non-parametric problem is reduced to a parametric one. The new model was tested on real data, and the forecast results were compared with classical models.
Keywords: stochastic functional differential equations, genetic algorithm, forecasting of financial processes, stochastic optimization.
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