This lecture is devoted to the problems of identification and prediction of deterministic chaos in economical time series. Deterministic chaos is a phenomenon that implies the possibility of short-term prediction, but excludes a long-term prediction. The lecture starts with a presentation of the mathematical tools (elements of the theory of chaotic dynamical systems) used in the research. The main part of the lecture, i.e. the identification of chaos, will be done according to the following steps: reconstruction of phase space, calculating a correlation dimension, calculating largest Lyapunov exponent, R/S analysis and  BDS test. The predictions wiil be done using  FNN method and radial basis functions. The analysis concerned with the daily log returns of ten stock market indexes and two automatically generated chaotic series (the series of the first coordinates of Henon map, and some logistic map). Also 12 series, obtained by the mixing of the previous series, were considered. The described research, on the one hand has not shown indisputably that chaos occurs in economical time series. On the other hand, it had been shown, that the considered series are essentially different from random series.

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