  In this research the technology of complex Markov chains is applied to
predict financial time series. The main distinction of complex or high-order
Markov Chains and simple first-order ones is the existing of aftereffect or
memory. The technology proposes prediction with the hierarchy of time
discretization intervals and splicing procedure for the prediction results at
the different frequency levels to the single prediction output time series. The
hierarchy of time discretizations gives a possibility to use fractal properties
of the given time series to make prediction on the different frequencies of the
series. The prediction results for world's stock market indices is presented.
