Comparative Analysis of Stock Bubble in S&P 500 Individual Stocks: A Study Using SADF and GSADF Models

Stock bubbles are characterized by unpredictable price surges and subsequent declines, causing significant losses for investors. This study investigates the effectiveness of the Generalized Sup Augmented Dickey–Fuller (GSADF) test in identifying mild explosive patterns and speculative bubbles within individual S&P 500 stocks, as compared to the Sup Augmented Dickey–Fuller (SADF) test. Utilizing real-time monitoring data, this research examines unit roots, stationarity, and the ability to detect multiple structural breaks. The GSADF test consistently outperforms the SADF test in rejecting the null hypothesis, demonstrating greater sensitivity and efficacy in recognizing stock bubbles. Monte Carlo simulations address size distortions in the GSADF test, enhancing accuracy.