The researchers developed a model called the LPPL model to detect bubbles in the Chinese stock market. They used this model to analyze two bubbles and subsequent crashes in Chinese stock indexes between 2005 and 2009. The model successfully predicted the timing of both crashes in advance. The researchers also used Lomb spectral analysis and unit-root tests to confirm the presence of bubbles in the market. The study shows that the LPPL model can accurately detect and predict financial bubbles in the stock market.