Модель случайного процесса c памятью

Abstract

The paper presents a model of a stochastic process with dependency on previous stales in for of a stochastic difference equation. This model complements the Brownian motion model to discribe the dynamics of financial assets prices. The type of dependence on previous states is derive from widely used financial time series analysis techniques that are applied to build up trader strategies. Presented estimation algorithms for model parameters are based on maximum likelihoc method. The analysis of model adequacy is conducted for real financial time series. The model determination and risk of one step forecasts are estimated.