Prediction of financial time series with the technology of high-order Markov chains

Abstract

In this research the technology of complex Markov chains, i.e. Markov chains with a memory is applied to forecast the financial time-series. 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. The algorithm of prediction includes the next steps: (1) Generate the hierarchical set of time discretizations; (2) Reducing the discretiza- tion of initial data and doing prediction at the every time-level (3) Recurrent conjunction of prediction series of different discretizations in a single time-series. The hierarchy of time discretizations gives a possibility to review long-memory properties of the series without increasing the order of the Markov chains, to make prediction on the different frequencies of the series. The technology is tested on several time-series, including: EUR/USD Forex course, the World’s indices, including Dow Jones, S&P 500, RTS, PFTS and other.