A method was developed to predict chaotic time series by analyzing their fractal structure and self-affine properties. The algorithm tracks the current trajectory of chaotic data and selects the most statistically self-similar segment. By constructing a prediction model based on attractors and coverage theorem, the model accurately predicts chaotic time series from various sources like Mackey-Glass, EEG signals, and Lorenz systems. This method effectively forecasts chaotic data, showing promising results for future applications.