A special type of the stochastic STOPBREAK process, which behaves properly when applied to time series data with emphatic permanent fluctuations, is presented. A good dynamic behavior is induced by the threshold regime and named the Split-BREAK process. General properties of this threshold STOPBREAK process are investigated, as well as some estimation procedures for the parameters of the process presented. A Monte Carlo simulation of the process is given and its application to the share trading on the Belgrade Stock Exchange illustrated.