Time series modeling and forecasting based on a Markov chain with changing transition matrices

•Markov models can be an effective way of prediction in time series.•The discretization of the state space is of importance for the quality of prediction.•Time windows grouped in sequences were used to obtain good transition matrices.•Good results of profit according to the Calmar criterion were obtained.•In order to optimize the current parameters of the method, machine learning was used. The subject of this research is prediction in a financial time series based on a model in the form of Markov chains. The essence of the considered algorithm is to create a sequence of time windows with a fixed length and a fixed division into intervals in the field of function values. The aim of the optimization consisting in finding the best window length, the number of windows and the number of intervals is to increase the predictive efficiency of the transition matrices. In the categories of expert systems, the presented computer program can be considered as imitating and replacing the investor in his manual activity and strongly supporting his mental effort. Two completely different time series were considered: the EUR/USD 1 h currency pair, and the WIG20 1d – the most important Polish stock exchange index. In both cases, the satisfactory adaptability of the proposed method was demonstrated, along with very good properties enabling the building of an effective investment strategy. Essential tests were performed for first-order Markov chains. These tests were also used for comparing the results of the study based on a Markov model of the second-order, which also achieved good results.