Financial time series prediction with the technology of complex Markov chains

Abstract

In this research the technology of complex Markov chains, i.e. Markov chains with a memory is applied to forecast financial time-series. The main distinction of complex or high-order Markov chains [1] and simple first-order ones is the existing of after effect or memory. The high-order Markov chains can be simplified to first-order ones by generalizing the states in Markov chains. Considering the “generalized state” as the sequence of states makes a possibility to model high-order Markov chains like first-order ones. The adaptive method of defining the states is proposed, it is concerned with the statistic properties of price returns [2]. According to the fundamental principles of quantum measurement theories, the measurement procedure impacts not only on the result of the measurement, but also on the state of the measured system, and the behaviour of this system in the future remains undefined, despite of the precision of the measurement. This statement, in our opinion, is general and is true not only for physical systems, but to any complex systems [3].