Modeling the Long-Term Economic Impact of Stock Market Bubbles: Analyzing DAX Volatility and Its Effects on German Real GDP Using Fractional Brownian Motion

This paper investigates the relationship between stock market dynamics and macroeconomic indicators, specifically focusing on the DAX index and German real GDP during a bubble period. By extending the Johansen-Ledoit-Sornette (JLS) model to incorporate fractional Brownian motion, we capture the long-memory properties of volatility. Our first model successfully estimates the DAX volatility during a speculative period using a FIGARCH(1,d,1) framework, revealing persistence in volatility. The second model explores how stock prices influence real GDP, demonstrating that prolonged volatility impacts macroeconomic performance. Our findings highlight the importance of accounting for financial market volatility in forecasting long-term economic stability. JEL Classification. G12, G15, E32, C22