摘要：The study of critical phenomena that originated in the natural sciences has been extended to the financial economics’ field, giving researchers new approaches to risk management, forecasting, the study of bubbles and crashes, and many kinds of problems involving complex systems with self-organized criticality (SOC). This study uses the theory of self-similar oscillatory time singularities to analyze stock market crashes. We test the Log Periodic Power Law/Model (LPPM) to analyze the Portuguese stock market, in its crises in 1998, 2007, and 2015. Parameter values are in line with those observed in other markets. This is particularly interesting since if the model performs robustly for Portugal, which is a small market with liquidity issues and the index is only composed of 20 stocks, we provide consistent evidence in favor of the proposed LPPM methodology. The LPPM methodology proposed here would have allowed us to avoid big loses in the 1998 Portuguese crash, and would have permitted us to sell at points near the peak in the 2007 crash. In the case of the 2015 crisis, we would have obtained a good indication of the moment where the lowest data point was going to be achieved.
