Famous models of conditional heteroscedasticity describe various effects of behavior of the financial markets. In this paper, we investigate the related model, called Split-ARCH, in some of its stochastic aspects, as the necessary and sufficient conditions of the strong stationarity and the estimation procedure. The basic asymptotic properties of those estimates are described, too. The most important segment of our work is dedicated to the practical issue of Split-ARCH model in analysis of the dynamics of the real data. We compared the Split-ARCH with standard models of ARCH type and showed that it was better stochastic model for the explanation of the world market prices of some precious metals.